🔬 Model Lab

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

---

### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

---

### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C

I'll solve each problem step-by-step.

**Problem 1:**

What is being asked: Find the target heart rate for a 26-year-old athlete, which is 80% of the maximum heart rate.

Step 1: Find the maximum heart rate.
- Maximum heart rate = 220 - age
- Maximum heart rate = 220 - 26 = 194 beats per minute

Step 2: Find 80% of the maximum heart rate.
- Target heart rate = 0.80 × 194 = 155.2 ≈ 155 beats per minute

ANSWER 1: B

---

**Problem 2:**

What is being asked: How many more seconds will Bob spend reading than Chandra when both read a 760-page book?

Step 1: Calculate Bob's reading time.
- Bob reads 1 page in 45 seconds
- Total time = 760 × 45 = 34,200 seconds

Step 2: Calculate Chandra's reading time.
- Chandra reads 1 page in 30 seconds
- Total time = 760 × 30 = 22,800 seconds

Step 3: Find the difference.
- Difference = 34,200 - 22,800 = 11,400 seconds

ANSWER 2: B

---

**Problem 3:**

What is being asked: Find the sum of two groups of numbers.

Step 1: Add the first group.
- 1 + 11 + 21 + 31 + 41 = 105

Step 2: Add the second group.
- 9 + 19 + 29 + 39 + 49 = 145

Step 3: Find the total.
- 105 + 145 = 250

ANSWER 3: E

---

**Problem 4:**

What is being asked: Find the sum of the prime factors of 2010.

Step 1: Factor 2010.
- 2010 = 2 × 1005
- 1005 = 5 × 201
- 201 = 3 × 67
- 67 is prime

So 2010 = 2 × 3 × 5 × 67

Step 2: Sum the prime factors.
- 2 + 3 + 5 + 67 = 77

ANSWER 4: C

---

**Problem 5:**

What is being asked: Find the height of a 1:20 scale model of the Capitol (actual height 289 feet).

Step 1: Apply the scale ratio.
- Model height = Actual height ÷ 20
- Model height = 289 ÷ 20 = 14.45 feet

Step 2: Round to the nearest whole number.
- 14.45 ≈ 14 feet

ANSWER 5: A

---

**Problem 6:**

What is being asked: Find the change from a $5 bill after buying 3 apples at 50 cents each.

Step 1: Calculate the cost.
- Cost = 3 × $0.50 = $1.50

Step 2: Calculate the change.
- Change = $5.00 - $1.50 = $3.50

ANSWER 6: E

---

**Problem 7:**

What is being asked: If February 13 is a Friday, what day is February 1?

Step 1: Count backward from February 13 to February 1.
- February 13 is a Friday
- February 1 is 12 days before February 13
- 12 days = 1 week + 5 days
- Going back 1 week from Friday = Friday
- Going back 5 more days: Thursday, Wednesday, Tuesday, Monday, Sunday
- So February 1 is a Sunday

ANSWER 7: A

---

**Problem 8:**

What is being asked: Find the sum of edges, corners, and faces of a cube.

Step 1: Count the features of a cube.
- Edges: 12
- Corners (vertices): 8
- Faces: 6

Step 2: Find the sum.
- 12 + 8 + 6 = 26

ANSWER 8: E

---

**Problem 9:**

What is being asked: If 20% of a number is 12, what is 30% of that number?

Step 1: Find the number.
- 0.20 × n = 12
- n = 12 ÷ 0.20 = 60

Step 2: Find 30% of the number.
- 0.30 × 60 = 18

ANSWER 9: B

---

**Problem 10:**

What is being asked: Find the carpet needed in square yards for a 12 ft × 9 ft floor.

Step 1: Find the area in square feet.
- Area = 12 × 9 = 108 square feet

Step 2: Convert to square yards.
- 1 yard = 3 feet, so 1 square yard = 9 square feet
- Area in square yards = 108 ÷ 9 = 12 square yards

ANSWER 10: A

---

**Problem 11:**

What is being asked: Calculate 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).

Step 1: Sum the arithmetic sequence.
- The sequence has 10 terms: 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
- Sum = (first + last) × count ÷ 2 = (81 + 99) × 10 ÷ 2 = 180 × 5 = 900

Step 2: Multiply by 2.
- 2 × 900 = 1800

ANSWER 11: E

---

**Problem 12:**

What is being asked: If 3/4 of a pitcher is poured equally into 5 cups, what percent of the pitcher's total capacity does each cup receive?

Step 1: Find the fraction each cup receives.
- Each cup receives (3/4) ÷ 5 = 3/20 of the pitcher

Step 2: Convert to a percentage.
- 3/20 = 0.15 = 15%

ANSWER 12: C

Problem 1:

The target heart rate is 80% of the maximum heart rate.

1. Find the maximum heart rate:
   \(220 - 26 = 194\)

2. Take 80% of that:
   \(0.8 \times 194 = 155.2\)

3. Round to the nearest whole number:
   \(155.2 \approx 155\)

So the target heart rate is 155 beats per minute.

ANSWER 1: B

Problem 2:

Bob reads 1 page in 45 seconds, and Chandra reads 1 page in 30 seconds.

For a 760-page book:

- Bob's time: \(760 \times 45 = 34{,}200\) seconds
- Chandra's time: \(760 \times 30 = 22{,}800\) seconds

Now find the difference:

\[
34{,}200 - 22{,}800 = 11{,}400
\]

So Bob spends 11,400 more seconds reading than Chandra.

ANSWER 2: B

Problem 3:

Compute each group separately.

First group:
\[
1+11+21+31+41 = 105
\]

Second group:
\[
9+19+29+39+49 = 145
\]

Add them:
\[
105+145 = 250
\]

ANSWER 3: E

Problem 4:

Factor 2010.

\[
2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67
\]

The prime factors are \(2, 3, 5,\) and \(67\).

Their sum is:
\[
2+3+5+67 = 77
\]

ANSWER 4: C

Problem 5:

The scale is \(1:20\), so the replica height is the real height divided by 20.

\[
289 \div 20 = 14.45
\]

Rounded to the nearest whole number:
\[
14
\]

ANSWER 5: A

Problem 6:

Each apple costs 50 cents, and Margie buys 3 apples:

\[
3 \times 50 = 150 \text{ cents} = \$1.50
\]

She pays with \$5.00, so the change is:

\[
5.00 - 1.50 = 3.50
\]

ANSWER 6: E

Problem 7:

Friday the 13th means the 13th day of the month is a Friday.

The 13th is 12 days after the 1st. Since \(12\) is a multiple of \(7\) plus \(5\), the day of the week advances by 5 days from the 1st to the 13th.

So if the 13th is Friday, then the 1st must be:

- Friday back 5 days = Sunday

Check:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday — yes, the 13th is Friday.

ANSWER 7: A

Problem 8:

Count each part of the cube:

- edges: 12
- corners: 8
- faces: 6

Add them:
\[
12+8+6 = 26
\]

ANSWER 8: E

Problem 9:

Let the number be \(x\).

20% of the number is 12:
\[
0.2x = 12
\]

Solve for \(x\):
\[
x = 60
\]

Now find 30% of 60:
\[
0.3 \times 60 = 18
\]

ANSWER 9: B

Problem 10:

First find the area in square feet:

\[
12 \times 9 = 108 \text{ square feet}
\]

Since \(1\) square yard \(= 3 \times 3 = 9\) square feet, convert:

\[
108 \div 9 = 12
\]

So the floor requires 12 square yards of carpet.

ANSWER 10: A

Problem 11:

There are 10 odd numbers from 81 to 99:

\[
81,83,85,87,89,91,93,95,97,99
\]

This is an arithmetic sequence with first term 81, last term 99, and 10 terms.

Sum:
\[
\frac{10(81+99)}{2} = 5 \cdot 180 = 900
\]

Then multiply by 2:

\[
2 \times 900 = 1800
\]

ANSWER 11: E

Problem 12:

Three fourths of the pitcher is full, so the amount of juice is \(\frac{3}{4}\) of the pitcher.

That amount is divided equally into 5 cups, so each cup gets:

\[
\frac{3/4}{5} = \frac{3}{20}
\]

Convert to percent:

\[
\frac{3}{20} = 0.15 = 15\%
\]

So each cup received 15% of the pitcher’s total capacity.

ANSWER 12: C

Problem 1:  
We are asked for the target heart rate, which is 80% of the maximum.  
- Maximum heart rate = 220 − age  
- Target heart rate = 0.80(220 − age)  
For age 26:  
Maximum = 220 − 26 = 194  
Target = 0.80 × 194 = 155.2  
Rounded to the nearest whole number: 155  
Tempting checks: 176 would be 0.8 of 220, but we must subtract age first.  

ANSWER 1: B

Problem 2:  
The novel has 760 pages.  
Reading times per page:  
- Alice: 20 s/page  
- Bob: 45 s/page  
- Chandra: 30 s/page  

Bob reads the whole book, and Chandra reads the whole book.  
So the difference comes from their different per-page speeds.

Total time for Bob = 760 × 45 = 34,200 seconds  
Total time for Chandra = 760 × 30 = 22,800 seconds  

Difference = 34,200 − 22,800 = 11,400 seconds  

ANSWER 2: B

Problem 3:  
We compute:  
(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)

First group:  
1 + 11 + 21 + 31 + 41 = (1+41) + (11+31) + 21  
= 42 + 42 + 21 = 105

Second group:  
9 + 19 + 29 + 39 + 49 = (9+49) + (19+39) + 29  
= 58 + 58 + 29 = 145

Total = 105 + 145 = 250  

ANSWER 3: E

Problem 4:  
Find the prime factorization of 2010, then add the prime factors (count multiplicity).

2010 = 2 × 1005  
1005 = 5 × 201  
201 = 3 × 67  

So: 2010 = 2 × 5 × 3 × 67  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77  

ANSWER 4: C

Problem 5:  
Scale ratio is 1:20, meaning model height = real height ÷ 20.  
Real height = 289 feet.  
Model height = 289 ÷ 20 = 14.45  

Rounded to nearest whole number: 14  

ANSWER 5: A

Problem 6:  
3 apples at 50 cents each:  
Cost = 3 × $0.50 = $1.50  

She paid with a $5 bill, so change = $5.00 − $1.50 = $3.50  

ANSWER 6: E

Problem 7:  
We’re told February contains Friday the 13th.  
That means the 13th is a Friday.  

Let’s track backwards:  
If Feb 13 is Friday, then Feb 12 is Thursday, and Feb 1 is:
13 − 1 = 12 days earlier.  
12 days = 2 weeks, so the day of the week stays the same.  
Therefore Feb 1 is also Friday.

But Friday is not among the choices, so we must re-check: February containing Friday the 13th does not specify which year—however the prompt asks: “If February is a month that contains Friday the 13th, what day of the week is February 1?”  
The weekday of Feb 1 is determined by the condition that Feb 13 is Friday.

If Feb 13 is Friday, then:
Feb 1 is 12 days before Friday → same weekday → Friday.

Since Friday isn’t listed, the only way a listed option could match is if the intended logic is that “February contains Friday the 13th” implies Feb 1 is **Thursday** only if they meant Feb 13 is Friday and the calendar counts differently—but standard counting gives Friday.

Checking the options: The correct day should be **Friday**, but not present. The closest consistent choice in common contest versions would be **Thursday** if the problem intended “Friday the 13th” to mean the *13th is Friday* and then asks Feb 2—but it asks Feb 1.

Given the provided choices, none are correct under standard calendar reasoning. However AMC-style problems always have a correct option, so we interpret:  
If February has Friday the 13th, then Feb 1 is **Sunday**? Let’s compute properly using mod 7:

Day of week shift from Feb 1 to Feb 13 is 12 days.  
12 mod 7 = 5.  
So Feb 13 weekday = Feb 1 weekday + 5 (mod 7).  
If Feb 13 is Friday, then Feb 1 is Friday − 5 days = (Friday -5) = Saturday?  
Let’s list:  
Friday -1 = Thursday  
-2 = Wednesday  
-3 = Tuesday  
-4 = Monday  
-5 = Sunday  

So Feb 1 is Sunday.

ANSWER 7: A

Problem 8:  
For a cube:  
- Number of edges = 12  
- Number of corners (vertices) = 8  
- Number of faces = 6  

Sum = 12 + 8 + 6 = 26  

ANSWER 8: E

Problem 9:  
If 20% of a number is 12, then the number is:  
Let the number be N.  
0.20N = 12  
N = 12 / 0.20 = 60  

Now 30% of N is:  
0.30 × 60 = 18  

ANSWER 9: B

Problem 10:  
Area of rectangle = length × width.  
Length = 12 ft, width = 9 ft.  
Area = 12 × 9 = 108 square feet.  

Convert to square yards:  
1 yard = 3 ft, so 1 square yard = (3 ft)² = 9 square feet.  
108 square feet ÷ 9 = 12 square yards.  

ANSWER 10: A

Problem 11:  
Compute:  
2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)

Inside parentheses are 10 odd numbers from 81 to 99 stepping by 2.  
Pair first and last:  
81 + 99 = 180  
83 + 97 = 180  
85 + 95 = 180  
87 + 93 = 180  
89 + 91 = 180  

There are 5 pairs, each summing to 180:  
Sum inside = 5 × 180 = 900  

Now multiply by 2:  
2 × 900 = 1800  

ANSWER 11: E

Problem 12:  
A pitcher is filled to 3/4.  
That filled amount is poured equally into 5 cups.

Each cup gets:  
(3/4) ÷ 5 = 3/4 × 1/5 = 3/20 of the total pitcher capacity.

Convert to percent:  
3/20 = 0.15 = 15%  

ANSWER 12: C

Problem 1:
1. Find the maximum heart rate: $220 - 26 = 194$.
2. Find the target heart rate (80% of max): $0.80 \times 194$.
3. Calculation: $194 \times 0.8 = 155.2$.
4. Rounding to the nearest whole number gives 155.
ANSWER 1: B

Problem 2:
1. Bob's time: $760 \text{ pages} \times 45 \text{ seconds/page} = 34,200 \text{ seconds}$.
2. Chandra's time: $760 \text{ pages} \times 30 \text{ seconds/page} = 22,800 \text{ seconds}$.
3. Difference: $34,200 - 22,800 = 11,400 \text{ seconds}$.
ANSWER 2: B

Problem 3:
1. Sum the first group: $1 + 11 + 21 + 31 + 41 = 105$.
2. Sum the second group: $9 + 19 + 29 + 39 + 49 = 145$.
3. Total sum: $105 + 145 = 250$.
ANSWER 3: E

Problem 4:
1. Prime factorization of 2010: $2010 = 10 \times 201 = 2 \times 5 \times 3 \times 67$.
2. The prime factors are 2, 3, 5, and 67.
3. Sum of prime factors: $2 + 3 + 5 + 67 = 77$.
ANSWER 4: C

Problem 5:
1. The scale is $1:20$, so the replica height is $\frac{289}{20}$.
2. Calculation: $289 \div 20 = 14.45$.
3. Rounding to the nearest whole number gives 14.
ANSWER 5: A

Problem 6:
1. Cost of apples: $3 \times 0.50 = 1.50$ dollars.
2. Change: $5.00 - 1.50 = 3.50$ dollars.
ANSWER 6: E

Problem 7:
1. If Feb 13 is a Friday, count back 7 days to Feb 6 (Friday), then 7 days to Jan 30 (Friday).
2. Alternatively, count back from Feb 13: Feb 12 (Thu), Feb 11 (Wed), Feb 10 (Tue), Feb 9 (Mon), Feb 8 (Sun), Feb 7 (Sat), Feb 6 (Fri).
3. Feb 6 is Friday. Feb 5 (Thu), Feb 4 (Wed), Feb 3 (Tue), Feb 2 (Mon), Feb 1 (Sunday).
ANSWER 7: A

Problem 8:
1. Edges of a cube: 12.
2. Corners (vertices) of a cube: 8.
3. Faces of a cube: 6.
4. Sum: $12 + 8 + 6 = 26$.
ANSWER 8: E

Problem 9:
1. Let the number be $x$. $0.20x = 12 \implies x = \frac{12}{0.20} = 60$.
2. Find 30% of 60: $0.30 \times 60 = 18$.
ANSWER 9: B

Problem 10:
1. Area in square feet: $12 \times 9 = 108$ square feet.
2. Conversion: $1 \text{ yard} = 3 \text{ feet}$, so $1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}$.
3. Square yards required: $108 \div 9 = 12$.
ANSWER 10: A

Problem 11:
1. Sum the sequence: $81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99$.
2. This is an arithmetic series with 10 terms. Average = $\frac{81+99}{2} = 90$.
3. Sum = $90 \times 10 = 900$.
4. Multiply by 2: $900 \times 2 = 1800$.
ANSWER 11: E

Problem 12:
1. Total capacity is 100%. Juice is 75% of capacity.
2. Divide the juice into 5 cups: $75\% \div 5 = 15\%$.
ANSWER 12: C

Problem 1:
The maximum heart rate is found by subtracting the athlete's age from 220. For a 26-year-old, this is \(220 - 26 = 194\). The target heart rate is 80% of this value, so compute \(0.8 \times 194 = 155.2\). Rounded to the nearest whole number, this is 155. (Note that 194 itself appears as a choice but is the maximum rate, not the target; other percentages such as 70% or 90% of 194 do not match any listed choice.)

ANSWER 1: B

Problem 2:
Bob takes 45 seconds per page while Chandra takes 30 seconds per page. For a 760-page book the time difference per page is \(45 - 30 = 15\) seconds, so the total difference is \(760 \times 15 = 11400\) seconds.

ANSWER 2: B

Problem 3:
The first sum is \(1 + 11 + 21 + 31 + 41 = 105\). The second sum is \(9 + 19 + 29 + 39 + 49 = 145\). Adding these gives \(105 + 145 = 250\). Equivalently, pair terms across the two groups: each of the five pairs sums to 50, and \(5 \times 50 = 250\).

ANSWER 3: E

Problem 4:
Factorize \(2010 = 2 \times 3 \times 5 \times 67\). The distinct prime factors are 2, 3, 5 and 67; their sum is \(2 + 3 + 5 + 67 = 77\).

ANSWER 4: C

Problem 5:
A 1 : 20 scale model means the replica height is the real height divided by 20: \(289 / 20 = 14.45\). Rounded to the nearest whole number this is 14.

ANSWER 5: A

Problem 6:
Three apples at 50 cents each cost \(3 \times 0.50 = 1.50\) dollars. Paid with a 5-dollar bill, the change received is \(5 - 1.50 = 3.50\) dollars.

ANSWER 6: E

Problem 7:
February 13 is a Friday, so the day of February 1 is 12 days earlier. Since \(12 \equiv 5 \pmod{7}\), February 1 occurs 5 weekdays before Friday, which is Sunday.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 vertices and 6 faces. Their sum is \(12 + 8 + 6 = 26\).

ANSWER 8: E

Problem 9:
If 20% of a number equals 12, the number itself is \(12 / 0.2 = 60\). Then 30% of 60 is \(0.3 \times 60 = 18\).

ANSWER 9: B

Problem 10:
Convert dimensions to yards: 12 ft = 4 yd and 9 ft = 3 yd. The area is therefore \(4 \times 3 = 12\) square yards.

ANSWER 10: A

Problem 11:
The sum inside the parentheses consists of the ten consecutive odd integers from 81 to 99. Their average is \((81 + 99)/2 = 90\), so the sum is \(10 \times 90 = 900\). Multiplying by 2 yields \(2 \times 900 = 1800\).

ANSWER 11: E

Problem 12:
Three-fourths of the pitcher is divided equally among 5 cups, so each cup receives \((3/4) / 5 = 3/20\) of the pitcher's capacity. Converting to a percent gives \((3/20) \times 100 = 15\).

ANSWER 12: C

Problem 1:
To find the target heart rate of an athlete who is 26 years old, we need to first calculate the maximum heart rate and then find 80% of it. The maximum heart rate is calculated by subtracting the athlete's age from 220. So, the maximum heart rate = 220 - 26 = 194 beats per minute. Now, we need to find 80% of 194. To do this, we calculate 80% of 194 = 0.8 * 194 = 155.2. Rounding this to the nearest whole number gives us 155.

Let's examine the choices:
A. 134 is too low.
B. 155 matches our calculation.
C. 176 is too high.
D. 194 is the maximum heart rate, not the target heart rate.
E. 243 is too high.

ANSWER 1: B

Problem 2:
To determine how many more seconds Bob will spend reading than Chandra, we first need to calculate the time each of them takes to read the 760-page novel. Bob reads a page in 45 seconds, so he will take 760 * 45 seconds to read the whole book. Chandra reads a page in 30 seconds, so she will take 760 * 30 seconds. The difference in time = (760 * 45) - (760 * 30) = 760 * (45 - 30) = 760 * 15 = 11,400 seconds.

Let's examine the choices:
A. 7,600 is too low.
B. 11,400 matches our calculation.
C. 12,500 is too high.
D. 15,200 is too high.
E. 22,800 is too high.

ANSWER 2: B

Problem 3:
To solve the given expression, (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49), let's first simplify each part. 
First part: 1 + 11 + 21 + 31 + 41 = 105.
Second part: 9 + 19 + 29 + 39 + 49 = 145.
Adding them together: 105 + 145 = 250.

Let's examine the choices:
A. 150 is too low.
B. 199 is too low.
C. 200 is too low.
D. 249 is too low.
E. 250 matches our calculation.

ANSWER 3: E

Problem 4:
To find the sum of the prime factors of 2010, we first need to factorize 2010 into its prime factors. 
2010 = 2 * 1005 = 2 * 3 * 335 = 2 * 3 * 5 * 67.
So, the prime factors are 2, 3, 5, and 67. The sum of these prime factors = 2 + 3 + 5 + 67 = 77.

Let's examine the choices:
A. 67 is too low and is one of the prime factors.
B. 75 is too low.
C. 77 matches our calculation.
D. 201 is too high.
E. 210 is too high.

ANSWER 4: C

Problem 5:
The height of the United States Capitol is 289 feet, and the scale model has a ratio of 1 : 20. To find the height of the replica, we divide the actual height by 20. So, the height of the replica = 289 / 20 = 14.45 feet. Rounding this to the nearest whole number gives us 14 feet.

Let's examine the choices:
A. 14 matches our calculation.
B. 15 is too high.
C. 16 is too high.
D. 18 is too high.
E. 20 is too high.

ANSWER 5: A

Problem 6:
Margie bought 3 apples at 50 cents per apple. So, the total cost = 3 * 50 cents = $1.50. She paid with a $5 bill. The change she received = $5 - $1.50 = $3.50.

Let's examine the choices:
A. $1.50 is too low.
B. $2.00 is too low.
C. $2.50 is too low.
D. $3.00 is too low.
E. $3.50 matches our calculation.

ANSWER 6: E

Problem 7:
If February contains Friday the 13th, we need to determine what day of the week February 1 is. To do this, we count backwards from the 13th. 
13th is a Friday, 
12th is a Thursday, 
11th is a Wednesday, 
10th is a Tuesday, 
9th is a Monday, 
8th is a Sunday, 
7th is a Saturday, 
6th is a Friday, 
5th is a Thursday, 
4th is a Wednesday, 
3rd is a Tuesday, 
2nd is a Monday, 
1st is a Sunday.

Let's examine the choices:
A. Sunday matches our calculation.
B. Monday is incorrect.
C. Wednesday is incorrect.
D. Thursday is incorrect.
E. Saturday is incorrect.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners, and 6 faces. Jamie counted the edges (12), Jimmy counted the corners (8), and Judy counted the faces (6). The sum of their counts = 12 + 8 + 6 = 26.

Let's examine the choices:
A. 12 is too low.
B. 16 is too low.
C. 20 is too low.
D. 22 is too low.
E. 26 matches our calculation.

ANSWER 8: E

Problem 9:
If 20% of a number is 12, we need to find 30% of the same number. First, let's find the number. 
20% of x = 12 => 0.2x = 12 => x = 12 / 0.2 = 60.
Now, 30% of 60 = 0.3 * 60 = 18.

Let's examine the choices:
A. 15 is too low.
B. 18 matches our calculation.
C. 20 is too high.
D. 24 is too high.
E. 30 is too high.

ANSWER 9: B

Problem 10:
The rectangular floor is 12 feet long and 9 feet wide. To find the area in square feet, we multiply the length by the width: 12 * 9 = 108 square feet. Since there are 3 feet in a yard, 1 square yard = 3 * 3 = 9 square feet. To convert square feet to square yards, we divide by 9. So, 108 / 9 = 12 square yards.

Let's examine the choices:
A. 12 matches our calculation.
B. 36 is too high.
C. 108 is the area in square feet, not square yards.
D. 324 is too high.
E. 972 is too high.

ANSWER 10: A

Problem 11:
To solve 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99), let's first simplify the expression inside the parentheses. 
The series inside the parentheses is an arithmetic series with the first term = 81, last term = 99, and the number of terms = 10. 
The sum of an arithmetic series = n/2 * (first term + last term) = 10/2 * (81 + 99) = 5 * 180 = 900.
Now, 2 * 900 = 1800.

Let's examine the choices:
A. 1600 is too low.
B. 1650 is too low.
C. 1700 is too low.
D. 1750 is too low.
E. 1800 matches our calculation.

ANSWER 11: E

Problem 12:
Three fourths of the pitcher is filled with pineapple juice, which means it is 3/4 full. When this amount is poured equally into 5 cups, each cup gets (3/4) / 5 = 3/20 of the pitcher's total capacity. To find the percentage, we convert 3/20 into a percentage: (3/20) * 100 = 15%.

Let's examine the choices:
A. 5 is too low.
B. 10 is too low.
C. 15 matches our calculation.
D. 20 is too high.
E. 25 is too high.

ANSWER 12: C

**Problem 1:**
The theoretical maximum heart rate is \(220 - 26 = 194\) beats per minute.  
The target heart rate is \(80\%\) of this: \(0.80 \times 194 = 155.2\).  
To the nearest whole number, this is 155.  
**ANSWER 1: B**

**Problem 2:**
Bob reads at 45 seconds per page, so his total time for 760 pages is \(760 \times 45 = 34\,200\) seconds.  
Chandra reads at 30 seconds per page, so her total time is \(760 \times 30 = 22\,800\) seconds.  
The difference is \(34\,200 - 22\,800 = 11\,400\) seconds.  
**ANSWER 2: B**

**Problem 3:**
Group the pairs: \((1+9) + (11+19) + (21+29) + (31+39) + (41+49) = 10 + 30 + 50 + 70 + 90 = 250\).  
Alternatively, \(1+11+21+31+41 = 105\) and \(9+19+29+39+49 = 145\); \(105+145 = 250\).  
**ANSWER 3: E**

**Problem 4:**
Factor \(2010\):  
\(2010 = 2 \times 1005 = 2 \times 3 \times 335 = 2 \times 3 \times 5 \times 67\).  
The prime factors are 2, 3, 5, and 67. Their sum is \(2+3+5+67 = 77\).  
**ANSWER 4: C**

**Problem 5:**
The scale is \(1 : 20\), so the model height is \(289 \div 20 = 14.45\) feet.  
Rounded to the nearest whole number, this is 14 feet.  
**ANSWER 5: A**

**Problem 6:**
Cost of 3 apples at 50 cents each: \(3 \times 0.50 = \$1.50\).  
Paid with a \$5 bill: change is \(5.00 - 1.50 = \$3.50\).  
**ANSWER 6: E**

**Problem 7:**
If the 13th is a Friday, then the 1st is 12 days earlier.  
\(12 \div 7 = 1\) remainder 5, so go back 5 days from Friday: Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8) — wait, let's count back carefully.  
Friday (13), Thursday (12), Wednesday (11), Tuesday (10), Monday (9), Sunday (8), Saturday (7), Friday (6), Thursday (5), Wednesday (4), Tuesday (3), Monday (2), Sunday (1). So February 1 is a Sunday.  
**ANSWER 7: A**

**Problem 8:**
A cube has 12 edges, 8 vertices (corners), and 6 faces. Sum = \(12 + 8 + 6 = 26\).  
**ANSWER 8: E**

**Problem 9:**
\(20\%\) of the number is 12, so the number is \(12 \div 0.20 = 60\).  
\(30\%\) of 60 is \(0.30 \times 60 = 18\).  
**ANSWER 9: B**

**Problem 10:**
Floor area in square feet: \(12 \times 9 = 108\) ft².  
Since 1 yard = 3 feet, \(1 \text{ yd}^2 = 9 \text{ ft}^2\).  
Area in square yards: \(108 \div 9 = 12\).  
**ANSWER 10: A**

**Problem 11:**
The sum of the odd numbers from 81 to 99: there are 10 terms, average is \((81+99)/2 = 90\).  
Sum = \(10 \times 90 = 900\).  
Multiply by 2: \(2 \times 900 = 1800\).  
**ANSWER 11: E**

**Problem 12:**
The pitcher is \(\frac{3}{4}\) full. Dividing equally among 5 cups gives each cup \(\frac{3/4}{5} = \frac{3}{20}\) of the pitcher.  
As a percent: \(\frac{3}{20} \times 100\% = 15\%\).  
**ANSWER 12: C**

Problem 1:
We need to find the target heart rate for a 26-year-old athlete.
- Step 1: Find the maximum heart rate: 220 − 26 = 194 beats per minute.
- Step 2: Find 80% of the maximum: 0.80 × 194 = 155.2 beats per minute.
- Step 3: Round to the nearest whole number: 155.
- Ruling out others: Choice D (194) is the maximum heart rate itself (forgetting to take 80%). Choice C (176) would come from using a different age. Choice A (134) might come from taking 80% of a wrong base.
ANSWER 1: B

Problem 2:
We need to find how many more seconds Bob spends reading than Chandra.
- Step 1: Bob's total reading time = 760 pages × 45 seconds/page = 34,200 seconds.
- Step 2: Chandra's total reading time = 760 pages × 30 seconds/page = 22,800 seconds.
- Step 3: Difference = 34,200 − 22,800 = 11,400 seconds.
- Shortcut: Difference = 760 × (45 − 30) = 760 × 15 = 11,400.
- Ruling out others: Choice A (7,600) is 760 × 10. Choice E (22,800) is Chandra's total time. Choice D (15,200) is 760 × 20.
ANSWER 2: B

Problem 3:
We need to compute (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
- Strategy: Pair terms from the two groups that sum to a round number.
  - 1 + 49 = 50
  - 11 + 39 = 50
  - 21 + 29 = 50
  - 31 + 19 = 50
  - 41 + 9 = 50
- Total = 50 + 50 + 50 + 50 + 50 = 5 × 50 = 250.
- Verification by direct addition: First group = 105, second group = 145, sum = 250.
- Ruling out others: Choice C (200) might come from miscounting pairs. Choice D (249) is an off-by-one error.
ANSWER 3: E

Problem 4:
We need the sum of the prime factors of 2010.
- Step 1: Factor 2010.
  - 2010 is even: 2010 = 2 × 1005
  - 1005 ends in 5: 1005 = 5 × 201
  - 201: sum of digits = 3, so divisible by 3: 201 = 3 × 67
  - 67 is prime (not divisible by 2, 3, 5, or 7; and 8² = 64 < 67 < 81 = 9²).
- Step 2: Prime factorization: 2010 = 2 × 3 × 5 × 67.
- Step 3: Sum of prime factors = 2 + 3 + 5 + 67 = 77.
- Ruling out others: Choice E (210) is 2 × 3 × 5 × 7 (wrong factorization). Choice B (75) would be missing the 2.
ANSWER 4: C

Problem 5:
We need the height of a 1:20 scale model of the U.S. Capitol (289 feet tall).
- Step 1: Model height = 289 ÷ 20 = 14.45 feet.
- Step 2: Round to the nearest whole number: 14.45 rounds to 14.
- Ruling out others: Choice B (15) would result from rounding 14.5 up, but 14.45 is closer to 14. Choice C (16) might come from dividing by 18 instead of 20.
ANSWER 5: A

Problem 6:
We need to find Margie's change.
- Step 1: Total cost = 3 apples × $0.50/apple = $1.50.
- Step 2: Change = $5.00 − $1.50 = $3.50.
- Ruling out others: Choice A ($1.50) is the cost, not the change. Choice C ($2.50) might come from subtracting from $4.00 by mistake.
ANSWER 6: E

Problem 7:
We need to find the day of the week for February 1, given that February 13 is a Friday.
- Step 1: February 1 is 12 days before February 13.
- Step 2: 12 days = 1 week and 5 days. Going back 1 full week from Friday lands on Friday again. Then go back 5 more days.
- Step 3: Count backward 5 days from Friday: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5).
- So February 1 is a Sunday.
- Ruling out others: Choice B (Monday) would be going back 4 days. Choice E (Saturday) would be going back 6 days.
ANSWER 7: A

Problem 8:
We need the sum of the number of edges, corners (vertices), and faces of a cube.
- Edges of a cube: 12 (4 on top, 4 on bottom, 4 vertical)
- Corners (vertices) of a cube: 8 (4 on top, 4 on bottom)
- Faces of a cube: 6 (top, bottom, front, back, left, right)
- Sum = 12 + 8 + 6 = 26.
- Ruling out others: Choice C (20) might come from forgetting one category. Choice D (22) might come from miscounting edges as 10.
ANSWER 8: E

Problem 9:
We need to find 30% of a number, given that 20% of it is 12.
- Method 1: Find the number first. 0.20 × x = 12, so x = 12 ÷ 0.20 = 60. Then 30% of 60 = 0.30 × 60 = 18.
- Method 2 (proportional): 30% is 30/20 = 1.5 times 20%. So 30% of the number = 1.5 × 12 = 18.
- Ruling out others: Choice A (15) might come from adding 3 to 12. Choice D (24) would be 40% of the number.
ANSWER 9: B

Problem 10:
We need the area in square yards of a 12 ft × 9 ft floor.
- Step 1: Convert dimensions to yards. Since 3 feet = 1 yard:
  - Length = 12 ÷ 3 = 4 yards
  - Width = 9 ÷ 3 = 3 yards
- Step 2: Area = 4 × 3 = 12 square yards.
- Alternative: Area in sq ft = 12 × 9 = 108 sq ft. Since 1 sq yd = 3 × 3 = 9 sq ft, area = 108 ÷ 9 = 12 sq yd.
- Ruling out others: Choice C (108) is the area in square feet (forgot to convert). Choice B (36) might come from dividing 108 by 3 instead of 9.
ANSWER 10: A

Problem 11:
We need to compute 2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
- Step 1: The sum inside is an arithmetic sequence with first term a = 81, last term l = 99, and n = 10 terms.
- Step 2: Sum = n × (a + l) / 2 = 10 × (81 + 99) / 2 = 10 × 180 / 2 = 10 × 90 = 900.
- Step 3: Multiply by 2: 2 × 900 = 1800.
- Alternative pairing: (81+99) + (83+97) + (85+95) + (87+93) + (89+91) = 180 × 5 = 900. Then 2 × 900 = 1800.
- Ruling out others: Choice C (1700) might come from a pairing error. Choice D (1750) might come from miscounting terms.
ANSWER 11: E

Problem 12:
We need to find what percent of the pitcher's total capacity each cup receives.
- Step 1: The pitcher is 3/4 full. This juice is divided equally among 5 cups.
- Step 2: Each cup receives (3/4) ÷ 5 = 3/20 of the total capacity.
- Step 3: Convert to percent: 3/20 = 15/100 = 15%.
- Ruling out others: Choice B (10%) would be if the pitcher were half full (1/2 ÷ 5 = 1/10). Choice D (20%) would be if the pitcher were completely full (1 ÷ 5 = 1/5). Choice E (25%) might come from dividing 100% by 4 instead of considering the 5 cups.
ANSWER 12: C

 Problem 1:
The problem asks for an athlete’s target heart rate at age 26. The maximum heart rate is defined as $220$ minus the athlete’s age, and the target rate is $80\%$ of that maximum.

- Compute the maximum heart rate:
  $$220 - 26 = 194 \text{ beats per minute}$$
- Compute $80\%$ of the maximum:
  $$0.80 \times 194 = 155.2 \text{ beats per minute}$$
- Round to the nearest whole number:
  $$155.2 \approx 155$$

It is tempting to choose $176$ (choice C), but that is $80\%$ of $220$, forgetting to subtract the age first. $194$ (choice D) is the maximum heart rate itself, not the target.

ANSWER 1: B

Problem 2:
Bob and Chandra each read the entire $760$-page novel. Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds. We need to find how many more seconds Bob spends reading than Chandra.

- Bob’s total time: $760 \times 45$ seconds
- Chandra’s total time: $760 \times 30$ seconds
- Extra time Bob spends:
  $$760 \times (45 - 30) = 760 \times 15$$
  $$760 \times 10 = 7{,}600$$
  $$760 \times 5 = 3{,}800$$
  $$7{,}600 + 3{,}800 = 11{,}400 \text{ seconds}$$

Choice A ($7{,}600$) is $760 \times 10$, using the wrong time difference. Choice D ($15{,}200$) is $760 \times 20$. Choice E ($22{,}800$) is Chandra’s total reading time, not the difference.

ANSWER 2: B

Problem 3:
We must evaluate the sum of the two grouped expressions:
$$(1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49)$$

Instead of adding each group separately, pair the terms from the first and second groups:
- $1 + 49 = 50$
- $11 + 39 = 50$
- $21 + 29 = 50$
- $31 + 19 = 50$
- $41 + 9 = 50$

There are five pairs, each summing to $50$:
$$5 \times 50 = 250$$

Choice C ($200$) is too low; it might arise from dropping a pair or a carry. Choice D ($249$) is close but incorrect. Choice A ($150$) misses half the sum.

ANSWER 3: E

Problem 4:
We need the sum of the prime factors of $2010$.

- Factor $2010$:
  $$2010 = 2 \times 1005$$
  $$1005 = 3 \times 335$$
  $$335 = 5 \times 67$$
  $67$ is prime.
- So $2010 = 2 \times 3 \times 5 \times 67$.
- Sum of distinct prime factors:
  $$2 + 3 + 5 + 67 = 77$$

Choice B ($75$) is the sum if the factor $2$ is forgotten. Choice A ($67$) is just the largest prime factor. Choice D ($201$) and E ($210$) are not related to the sum of the prime factors.

ANSWER 4: C

Problem 5:
A scale model has ratio $1:20$. The real Capitol is $289$ feet tall. Find the replica’s height in feet, rounded to the nearest whole number.

- Replica height $= \dfrac{289}{20} = 14.45$ feet.
- Rounding $14.45$ to the nearest whole number gives $14$.

Choice B ($15$) might be chosen by incorrectly rounding $14.45$ upward. The other choices are far too large and could come from multiplying by $20$ or misplacing a decimal.

ANSWER 5: A

Problem 6:
Margie bought $3$ apples at $50$ cents each and paid with a $\$5$ bill. How much change did she receive?

- Cost of apples:
  $$3 \times \$0.50 = \$1.50$$
- Change from a $\$5$ bill:
  $$\$5.00 - \$1.50 = \$3.50$$

Choice A ($\$1.50$) is the total cost, not the change. Choice C ($\$2.50$) might come from miscalculating the cost as $\$2.50$.

ANSWER 6: E

Problem 7:
If February contains a Friday the $13$th, what day of the week is February $1$?

- February $13$ is a Friday.
- February $1$ is $12$ days earlier than February $13$.
- Since $12 = 7 + 5$, going back $12$ days is the same as going back $5$ days from Friday.
- Counting backward: Thursday ($1$), Wednesday ($2$), Tuesday ($3$), Monday ($4$), Sunday ($5$).

Thus February $1$ falls on a Sunday.

Checking: If Feb $1$ is Sunday, then Feb $8$ is also Sunday, and Feb $13$ is Friday — this matches. Choice B (Monday) is off by one day. Choice C (Wednesday) would make Feb $13$ a Tuesday.

ANSWER 7: A

Problem 8:
Jamie counted the edges, Jimmy the corners (vertices), and Judy the faces of a cube. We need the sum of these three numbers.

- A cube has $12$ edges.
- A cube has $8$ corners (vertices).
- A cube has $6$ faces.
- Sum:
  $$12 + 8 + 6 = 26$$

Choice D ($22$) is edges plus faces only ($12+6+4$? No, $12+6+4$ is wrong; actually $12+8+2$? Not sure). Choice C ($20$) is edges plus vertices ($12+8$). Choice A ($12$) counts only edges.

ANSWER 8: E

Problem 9:
If $20\%$ of a number is $12$, what is $30\%$ of the same number?

Method 1: Find the whole number first.
- Let the number be $x$.
- $0.20x = 12 \Rightarrow x = 12 \div 0.20 = 60$.
- $30\%$ of $60$: $0.30 \times 60 = 18$.

Method 2: Use ratios directly.
- $30\%$ is $1.5$ times $20\%$.
- $1.5 \times 12 = 18$.

Choice A ($15$) might come from adding $3$ to $12$. Choice D ($24$) is double $12$. Choice E ($30$) could come from misreading the percentage.

ANSWER 9: B

Problem 10:
A floor measures $12$ feet by $9$ feet. Carpet is sold by the square yard. How many square yards are needed? ($3$ feet $= 1$ yard)

Method 1: Convert dimensions first.
- Length: $12 \text{ ft} = 4 \text{ yd}$.
- Width: $9 \text{ ft} = 3 \text{ yd}$.
- Area: $4 \times 3 = 12$ square yards.

Method 2: Convert area.
- Area in square feet: $12 \times 9 = 108 \text{ sq ft}$.
- Since $1 \text{ sq yd} = 3 \times 3 = 9 \text{ sq ft}$:
  $$108 \div 9 = 12 \text{ sq yd}$$

Choice C ($108$) is the area in square feet. Choice B ($36$) comes from dividing by $3$ instead of $9$. Choice D ($324$) is $108 \times 3$.

ANSWER 10: A

Problem 11:
Evaluate:
$$2(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99)$$

The numbers inside form an arithmetic sequence with $10$ terms, first term $81$ and last term $99$.

- Sum of an arithmetic sequence $= \dfrac{\text{number of terms}}{2} \times (\text{first} + \text{last})$
- Sum inside parentheses:
  $$\frac{10}{2} \times (81 + 99) = 5 \times 180 = 900$$
- Multiply by $2$:
  $$2 \times 900 = 1800$$

Choice A ($1600$) might come from using $8$ terms or an incorrect average. Choice B ($1650$) and D ($1750$) are plausible-looking arithmetic errors. Choice E ($1800$) is correct.

ANSWER 11: E

Problem 12:
The pitcher is $\frac34$ full of juice. This juice is divided equally 

Problem 1:
We need the target heart rate for a 26-year-old athlete. The theoretical maximum heart rate is 220 minus age: 220 - 26 = 194 beats per minute. The target is 80% of this: 0.80 × 194 = 155.2. Rounding to the nearest whole number gives 155. The choices include 155 (B). Other choices: 134 would be 80% of 167.5, 176 would be 80% of 220, 194 is the max, 243 is too high. So answer is B.

ANSWER 1: B

Problem 2:
The novel has 760 pages. Bob reads a page in 45 seconds, so his total time is 760 × 45 = 34,200 seconds. Chandra reads a page in 30 seconds, so her total time is 760 × 30 = 22,800 seconds. The difference is 34,200 - 22,800 = 11,400 seconds. That matches choice B. Other choices: 7,600 would be 760×10, 12,500 is not correct, 15,200 would be 760×20, 22,800 is Chandra's time.

ANSWER 2: B

Problem 3:
Compute the two sums separately. First group: 1+11+21+31+41 = (1+41)=42, (11+31)=42, plus 21 gives 42+42+21=105. Second group: 9+19+29+39+49 = (9+49)=58, (19+39)=58, plus 29 gives 58+58+29=145. Total = 105+145=250. So answer E. Other choices: 150, 199, 200, 249 are not 250.

ANSWER 3: E

Problem 4:
Find the prime factors of 2010. 2010 = 2 × 1005 = 2 × 5 × 201 = 2 × 5 × 3 × 67. So the prime factors are 2, 3, 5, 67. Their sum is 2+3+5+67 = 77. That's choice C. 67 is one factor alone, 75 is 2+3+5+65? No, 77 is correct.

ANSWER 4: C

Problem 5:
Scale ratio is 1:20, meaning the replica is 1/20 the size of the real building. The Capitol is 289 feet tall, so replica height = 289 ÷ 20 = 14.45 feet. Rounded to the nearest whole number gives 14 feet. That's choice A. 15 would be rounding up, 16, 18, 20 are too high.

ANSWER 5: A

Problem 6:
Cost per apple = 50 cents = $0.50. For 3 apples, total cost = 3 × $0.50 = $1.50. She pays with a $5 bill, so change = $5.00 - $1.50 = $3.50. That's choice E. Other choices: $1.50 is the cost, $2.00, $2.50, $3.00 are not correct.

ANSWER 6: E

Problem 7:
February contains Friday the 13th. The day of the week for February 1 is 12 days earlier than February 13. Since days repeat every 7 days, subtract 12 mod 7 = 5 days from Friday. Friday minus 5 days: Thursday (1), Wednesday (2), Tuesday (3), Monday (4), Sunday (5). So February 1 is Sunday. Check: If Feb 1 is Sunday, then Feb 8 is Sunday, Feb 13 is Friday (since 13-8=5 days after Sunday = Friday). So answer A. Other days would not give Friday the 13th.

ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. The sum is 12 + 8 + 6 = 26. That's choice E. Other sums: 12, 16, 20, 22 are too low.

ANSWER 8: E

Problem 9:
Let the number be x. 20% of x is 12 → 0.20x = 12 → x = 12 / 0.20 = 60. Then 30% of x is 0.30 × 60 = 18. So answer B. Other choices: 15 would be 25% of 60, 20 is 33.3%, 24 is 40%, 30 is 50%.

ANSWER 9: B

Problem 10:
The floor is 12 feet by 9 feet. Since 3 feet = 1 yard, convert: length = 12/3 = 4 yards, width = 9/3 = 3 yards. Area in square yards = 4 × 3 = 12. So answer A. Other choices: 36 would be 6×6, 108 would be 12×9 in feet, 324 and 972 are much larger.

ANSWER 10: A

Problem 11:
The expression is 2 times the sum of an arithmetic series: 81, 83, ..., 99. There are 10 terms (since (99-81)/2+1 = 10). The average of first and last is (81+99)/2 = 90. Sum of the series = 10 × 90 = 900. Then multiply by 2 gives 1800. So answer E. Other choices: 1600, 1650, 1700, 1750 are not 1800.

ANSWER 11: E

Problem 12:
The pitcher is 3/4 full of juice. This juice is poured equally into 5 cups. So each cup gets (3/4) ÷ 5 = 3/20 of the pitcher's total capacity. As a percent, (3/20) × 100% = 15%. So answer C. Other choices: 5% would be 1/20, 10% would be 2/20, 20% would be 4/20, 25% would be 5/20.

ANSWER 12: C

**Problem 1:**  
Target heart rate = 80 % of (220 – age).  
Age = 26 → max heart rate = 220 – 26 = 194 bpm.  
Target = 0.80 × 194 = 155.2 ≈ 155 bpm.  

ANSWER 1: B  

---

**Problem 2:**  
Bob reads a page in 45 s, Chandra in 30 s.  
Time for Bob = 760 pages × 45 s = 34 200 s.  
Time for Chandra = 760 pages × 30 s = 22 800 s.  
Difference = 34 200 – 22 800 = 11 400 s.  

ANSWER 2: B  

---

**Problem 3:**  
First sum: 1 + 11 + 21 + 31 + 41 = 105.  
Second sum: 9 + 19 + 29 + 39 + 49 = 145.  
Total = 105 + 145 = 250.  

ANSWER 3: E  

---

**Problem 4:**  
Factor 2010: 2010 = 2 × 3 × 5 × 67.  
Prime factors are 2, 3, 5, 67.  
Sum = 2 + 3 + 5 + 67 = 77.  

ANSWER 4: C  

---

**Problem 5:**  
Scale ratio 1 : 20.  
Replica height = 289 ft ÷ 20 = 14.45 ft → nearest whole number = 14 ft.  

ANSWER 5: A  

---

**Problem 6:**  
Cost of 3 apples at $0.50 each = $1.50.  
Change from $5.00 = $5.00 – $1.50 = $3.50.  

ANSWER 6: E  

---

**Problem 7:**  
If February 13 is a Friday, then February 1 is 12 days earlier.  
12 days = 1 week + 5 days, so subtract 5 days from Friday → Sunday.  

ANSWER 7: A  

---

**Problem 8:**  
Edges of a cube = 12, corners (vertices) = 8, faces = 6.  
Sum = 12 + 8 + 6 = 26.  

ANSWER 8: E  

---

**Problem 9:**  
Let the number be N. 20 % of N = 12 → 0.20 N = 12 → N = 60.  
30 % of N = 0.30 × 60 = 18.  

ANSWER 9: B  

---

**Problem 10:**  
Area of floor = 12 ft × 9 ft = 108 ft².  
1 yd = 3 ft → 1 yd² = 9 ft².  
Carpet needed = 108 ft² ÷ 9 ft²/yd² = 12 yd².  

ANSWER 10: A  

---

**Problem 11:**  
Sum inside parentheses: arithmetic series with 10 terms, first 81, last 99.  
Average = (81 + 99)/2 = 90.  
Sum = 90 × 10 = 900.  
Multiply by 2 → 1800.  

ANSWER 11: E  

---

**Problem 12:**  
Juice amount = 3/4 of pitcher.  
Divided into 5 cups → each cup gets (3/4) ÷ 5 = 3/20 of pitcher.  
Percent = (3/20) × 100 % = 15 %.  

ANSWER 12: C

Problem 1:  
The maximum heart rate is calculated by subtracting the athlete's age from 220:  
$220 - 26 = 194$ beats per minute.  
The target heart rate is 80% of this value:  
$0.80 \times 194 = 155.2$.  
Rounded to the nearest whole number, this is 155.  
ANSWER 1: B  

Problem 2:  
Bob reads 760 pages at 45 seconds per page:  
$760 \times 45 = 34,200$ seconds.  
Chandra reads 760 pages at 30 seconds per page:  
$760 \times 30 = 22,800$ seconds.  
The difference is $34,200 - 22,800 = 11,400$ seconds.  
ANSWER 2: B  

Problem 3:  
First group: $1 + 11 + 21 + 31 + 41 = 106$ (sum of arithmetic sequence with $a_1 = 1$, $d = 10$, $n = 5$: $S = \frac{5}{2}(2 \times 1 + 4 \times 10) = 105 + 1 = 106$).  
Second group: $9 + 19 + 29 + 39 + 49 = 145$ (similarly, $S = \frac{5}{2}(2 \times 9 + 4 \times 10) = 145$).  
Total: $106 + 145 = 251 - 1 = 250 - 0 = 250$ (direct summation confirms: $1+9=10$, $11+19=30$, ..., $41+49=90$; total $10+30+50+70+90=250$).  
ANSWER 3: E  

Problem 4:  
Prime factorization of 2010:  
$2010 \div 2 = 1005$; $1005 \div 3 = 335$; $335 \div 5 = 67$ (prime).  
Prime factors: $2, 3, 5, 67$.  
Sum: $2 + 3 + 5 + 67 = 77$.  
ANSWER 4: C  

Problem 5:  
Scale model ratio $1:20$.  
Actual height: 289 feet.  
Model height: $289 \div 20 = 14.45$.  
Rounded to nearest whole number: 14.  
ANSWER 5: A  

Problem 6:  
Cost of 3 apples: $3 \times 0.50 = 1.50$ dollars.  
Amount paid: 5 dollars.  
Change: $5.00 - 1.50 = 3.50$ dollars.  
ANSWER 6: E  

Problem 7:  
A Friday the 13th means February 13 is a Friday.  
Subtracting 12 days (multiple of 7: $12 \div 7 = 1$ week, 5 days remainder):  
Friday minus 5 days is Sunday.  
ANSWER 7: A  

Problem 8:  
Cube edges: 12.  
Cube corners: 8.  
Cube faces: 6.  
Sum: $12 + 8 + 6 = 26$.  
ANSWER 8: E  

Problem 9:  
Let the number be $x$.  
$0.20x = 12 \implies x = 60$.  
30% of 60: $0.30 \times 60 = 18$.  
ANSWER 9: B  

Problem 10:  
Floor area: $12 \times 9 = 108$ square feet.  
Convert to square yards: $108 \div 9 = 12$ (since 1 yard² = 9 feet²).  
ANSWER 10: A  

Problem 11:  
The sequence is arithmetic: first term 81, last term 99, 10 terms.  
Sum: $\frac{10}{2}(81 + 99) = 5 \times 180 = 900$.  
Multiply by 2: $2 \times 900 = 1800$.  
ANSWER 11: E  

Problem 12:  
Three-fourths of the pitcher: $\frac{3}{4}$.  
Divided equally into 5 cups: $\frac{3}{4} \div 5 = \frac{3}{20}$.  
As a percentage: $\frac{3}{20} \times 100 = 15\%$.  
ANSWER 12: C

### Problem 1:
What is being asked: Calculate an athlete's target heart rate, which is 80% of their maximum heart rate. Maximum heart rate = 220 - the athlete's age. The athlete is 26 years old; round the target to the nearest whole number.
Step 1: Calculate maximum heart rate: 220 - 26 = 194 bpm.
Step 2: Calculate 80% of the maximum: 0.8 * 194 = 155.2, which rounds to 155.
Wrong choice explanations: Option D (194) is the maximum heart rate, not the 80% target. Option C (176) is 80% of 220, forgetting to subtract the athlete's age. Options A and E are miscalculations.
ANSWER 1: B

---

### Problem 2:
What is being asked: Bob takes 45 seconds per page, Chandra takes 30 seconds per page to read a 760-page book. How many more seconds does Bob spend reading than Chandra?
Step 1: Calculate the per-page time difference: 45 - 30 = 15 seconds per page.
Step 2: Multiply by total pages to get the total difference: 15 * 760 = 11,400 seconds.
Wrong choice explanations: Option A (7600) uses an incorrect 10-second per-page difference. Option D (15200) is Chandra's total reading time, not the difference.
ANSWER 2: B

---

### Problem 3:
What is being asked: Calculate the sum of the two groups of numbers: (1 + 11 + 21 + 31 + 41) + (9 + 19 + 29 + 39 + 49).
Step 1: Pair terms to simplify addition: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 50 + 50 + 50 + 50 + 50 = 250.
Wrong choice explanations: Option C (200) is the result of adding incorrectly, underestimating the total. Option B (199) misses a carryover in manual addition.
ANSWER 3: E

---

### Problem 4:
What is being asked: Find the sum of the prime factors of 2010.
Step 1: Prime factorize 2010: 2010 = 2 * 3 * 5 * 67, all primes.
Step 2: Sum the factors: 2 + 3 + 5 + 67 = 77.
Wrong choice explanations: Option A (67) is only the largest prime factor, not the sum of all. Option B (75) omits the 2 in the sum of primes.
ANSWER 4: C

---

### Problem 5:
What is being asked: A scale model has a 1:20 ratio. The actual US Capitol is 289 feet tall. What is the height of the replica, rounded to the nearest whole number?
Step 1: Calculate the replica height: 289 / 20 = 14.45 feet.
Step 2: Round to the nearest whole number: 14.45 rounds down to 14, since the decimal is less than 0.5.
Wrong choice explanations: Option B (15) incorrectly rounds 14.45 up. Option E (20) uses an incorrect division of 289 by 15 instead of 20.
ANSWER 5: A

---

### Problem 6:
What is being asked: Margie buys 3 apples at 50 cents each, pays with a $5 bill. How much change does she get?
Step 1: Calculate total cost of apples: 3 * $0.50 = $1.50.
Step 2: Calculate change: $5.00 - $1.50 = $3.50.
Wrong choice explanations: Option A ($1.50) is the cost of the apples, not the change. Option C ($2.50) is the result of miscalculating the total apple cost.
ANSWER 6: E

---

### Problem 7:
What is being asked: If February has a Friday the 13th, what day of the week is February 1?
Step 1: The 13th is 12 days after the 1st. 12 days = 1 full week (7 days) plus 5 extra days.
Step 2: Count backwards 5 days from Friday: 5 days before Friday is Sunday. Verify: Feb 1 (Sunday) → Feb 8 (Sunday) → Feb13 (Friday), which matches the problem statement.
Wrong choice explanations: Option C (Wednesday) is the result of miscounting the number of days between the 1st and 13th.
ANSWER 7: A

---

### Problem 8:
What is being asked: Jamie counts a cube's edges, Jimmy counts its corners (vertices), Judy counts its faces. Sum the three numbers.
Step 1: A cube has 12 edges, 8 vertices, and 6 faces.
Step 2: Sum: 12 + 8 + 6 = 26.
Wrong choice explanations: Option C (20) forgets to add all three values correctly, usually missing the 12 edges.
ANSWER 8: E

---

### Problem 9:
What is being asked: If 20% of a number is 12, what is 30% of that same number?
Step 1: Find the full number: 0.2 * N = 12 → N = 12 / 0.2 = 60.
Step 2: Calculate 30% of 60: 0.3 * 60 = 18.
Wrong choice explanations: Option D (24) is 40% of 60, not 30%. Option A (15) is a miscalculation.
ANSWER 9: B

---

### Problem 10:
What is being asked: How many square yards of carpet are needed to cover a 12ft long, 9ft wide floor? 3 feet = 1 yard.
Step 1: Convert feet to yards: 12ft = 4 yards, 9ft = 3 yards.
Step 2: Calculate area: 4 * 3 = 12 square yards. Alternatively, calculate area in square feet (108 sq ft) and divide by 9 (number of sq ft in 1 sq yard) to get 12.
Wrong choice explanations: Option C (108) is the area in square feet, not square yards. Option B (36) is an incorrect unit conversion.
ANSWER 10: A

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### Problem 11:
What is being asked: Calculate 2*(81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99).
Step 1: Sum the terms inside the parentheses: pair terms to simplify: (81+99) + (83+97) + ... + (89+91) = 5 pairs of 180 = 900.
Step 2: Multiply by 2: 2 * 900 = 1800.
Wrong choice explanations: Option C (1700) undercounts the sum of the sequence inside the parentheses.
ANSWER 11: E

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### Problem 12:
What is being asked: 3/4 of a pitcher is full of juice, split equally into 5 cups. What percent of the pitcher's total capacity does each cup get?
Step 1: Calculate the fraction each cup receives: (3/4) / 5 = 3/20 = 0.15.
Step 2: Convert to percent: 0.15 = 15%. Verify: 75% of the pitcher's total is split into 5 cups, 75% / 5 = 15%.
Wrong choice explanations: Option D (20%) is what each cup would get if the full pitcher was split, not just 3/4.
ANSWER 12: C

Problem 1:
To find the target heart rate, first calculate the maximum heart rate for a 26-year-old: maximum = 220 - age = 220 - 26 = 194 beats per minute. The target is 80% of this maximum: 0.8 * 194 = 155.2, which rounds to 155.
ANSWER 1: B

Problem 2:
First find the time difference per page between Bob and Chandra: 45 - 30 = 15 seconds per page. For 760 pages, total extra time for Bob is 760 * 15 = 11,400 seconds.
ANSWER 2: B

Problem 3:
Group the terms into pairs that sum to 50: (1+49) + (11+39) + (21+29) + (31+19) + (41+9) = 5 * 50 = 250.
ANSWER 3: E

Problem 4:
Factorize 2010: 2010 = 2 * 1005 = 2 * 5 * 201 = 2 * 5 * 3 * 67. The prime factors are 2, 3, 5, 67. Their sum is 2 + 3 + 5 + 67 = 77.
ANSWER 4: C

Problem 5:
A 1:20 scale model means the model height is 1/20 of the real height. Real height is 289 feet, so model height = 289 / 20 = 14.45, which rounds to 14.
ANSWER 5: A

Problem 6:
Total cost of apples: 3 * $0.50 = $1.50. Change from $5 is 5.00 - 1.50 = $3.50.
ANSWER 6: E

Problem 7:
The 13th is 12 days after the 1st. 12 days = 1 week + 5 days, so the 1st is 5 days before the 13th. If the 13th is Friday, counting back 5 days: Friday → Thursday → Wednesday → Tuesday → Monday → Sunday. So February 1 is Sunday.
ANSWER 7: A

Problem 8:
A cube has 12 edges, 8 corners (vertices), and 6 faces. Sum: 12 + 8 + 6 = 26.
ANSWER 8: E

Problem 9:
If 20% of a number is 12, then 10% is 6, so 30% is 6 * 3 = 18.
ANSWER 9: B

Problem 10:
Convert feet to yards: 12 feet = 4 yards, 9 feet = 3 yards. Area in square yards is 4 * 3 = 12.
ANSWER 10: A

Problem 11:
The sum inside the parentheses is the sum of 10 odd numbers from 81 to 99. The average of the first and last term is (81 + 99)/2 = 90, so the sum is 10 * 90 = 900. Multiply by 2: 2 * 900 = 1800.
ANSWER 11: E

Problem 12:
3/4 of the pitcher is divided equally into 5 cups, so each cup gets (3/4) / 5 = 3/20 = 0.15 = 15% of the pitcher's total capacity.
ANSWER 12: C