Amanda plans to paint the 4 walls of her bedroom with 1 coat of paint. The walls are rectangular, and each wall measures 12 feet by 14 feet. She will not paint either the 3-foot-by-4-foot rectangular window in her bedroom or the 3-foot-by-7-foot rectangular bedroom door. Amanda knows that each gallon of paint covers between 350 and 400 square feet. If only 1-gallon cans of paint are available, which of the following is the minimum number of cans of paint Amanda needs to buy to paint her bedroom walls?

F. 1
G. 2
H. 3
J. 4
K. 5

Solution

The first step in solving this problem is to calculate the total surface area of Amanda’s room.

Each wall measures 12 by 14, so each wall has an area of 12×14 = 168.

There are 4 walls, so the total area is 168×4 = 672. Now, subtract the area that will not be painted: 3 × 4 = 12 for the window, and 3 × 7 = 21 for the door; 168 − 12 − 21 = 639.

Because Amanda needs to cover 639 square feet, and each can of paint covers 350 to 400 square feet, she will need a minimum of 2 cans of paint.

What is the largest integer less than \(\sqrt{42}\)?

A. 3
B. 6
C. 7
D. 9
E. 23

Solution

To quickly solve this problem, recall the perfect squares that are closest to \(\sqrt{42}\):

\(\sqrt{36}\) = 6

\(\sqrt{49}\) = 7

Because the question asks for the largest integer less than \(\sqrt{42}\), the correct answer must be 6.

A circular lamp base has a radius of 2.5 inches. When placed on a flat table, approximately how much area does the lamp base cover, in square inches?

F. 5.00
G. 6.25
H. 15.70
J. 19.63
K. 25.00

Solution

To solve this problem, use the formula for the area of a circle: A = πr²
Substitute 2.5 for the radius and solve (remember that π ≅ 3.14):

r = 2.5

A = π(2.5)²

A = π(6.25)

A ≅ 19.625 ≅ 19.63

Which of the following is the slope of a line parallel to the line y = ²⁄₅x + 7 in the standard (x, y) coordinate plane?

A. −7
B. −⁵⁄₂
C. ²⁄₅
D. 2
E. ⁵⁄₂

Solution

In the equation of a line, y = mx + b, m is the slope.

Recall that parallel lines have the same slope.

Therefore, because the slope of the given line is ²⁄₅, the slope of any line parallel to that line will also have a slope of ²⁄₅.

The total surface area of the rectangular solid shown below is the sum of the areas of the 6 sides. What is the solid’s total surface area, in square inches?

F. 18
G. 36
H. 48
J. 80
K. 96

Solution

To solve this problem, calculate the area of the sides:

Top/Bottom:

4 × 4 = 16

2(16) = 32

Sides:

3 × 4 = 12

4(12) = 48

32 + 48 = 80, the total surface area.

A poll of 200 students was taken before Center High School changed the name of its mascot. All 200 students indicated which 1 of the 4 mascot names they would vote for. The results of the poll are given in the table below.

If the poll is indicative of how the 3,000 students at Center High School will actually vote, which of the following is the best estimate of the number of votes Knights will receive?

A. 50
B. 200
C. 525
D. 750
E. 900

Solution

According to the information given in the table, 50 students voted for the name Knights.

Therefore, 50 out of 200 students polled voted for Knights.

First, calculate the percentage of those students polled who voted for Knights by setting up a proportion and solving for x, as follows:

50 students = x percent

200 students 100 percent

5, 000 = 200x

25 = x

You now know that 25% of the students polled voted for Lions.

You are given that there are 3,000 students at Center High School, so find 25% of 3,000:

3000 × 0.25 = 750

If the information in the table were converted to a pie chart, then the central angle of the sector for Lions would
measure how many degrees?

F. 144°
G. 108°
H. 72°
J. 54°
K. 45°

Solution

According to the information given in the table, 40 students voted for the name Lions.

Therefore, 40 out of 200 students voted for Lions.

First, calculate the percentage of the whole pie chart represented by Lions by setting up a proportion and solving for x, as follows:

40 students = x percent

200 students 100 percent

4, 000 = 200x

20 = x

You now know that 20% of the students voted for Lions.

Because there are 360° in a circle, find 20% of 360:

360 × 0.2 = 72

What percent of the students polled chose Spartans in the poll?

A. 40%
B. 30%
C. 25%
D. 20%
E. 15%

Solution

According to the information given in the table, 30 students voted for the name Spartans.

Therefore, 30 out of 200 students voted for Spartans. Because you are looking for a percentage, set up a proportion and solve for x, as follows:

30 students = x percent

200 students 100 percent

3, 000 = 200x

15 = x

Given the triangle shown below with exterior angles that measure a˚, b˚, and c˚ as shown, what is the sum of a, b, and c?

F. 180
G. 236
H. 261
J. 360
K. Cannot be determined from the given information

Solution

If you recognized that a, b, and c are supplementary to the interior angles of the triangle, you could have quickly arrived at the correct answer: a + c = 180; a + b = 180;b + c = 180; therefore, a + b + c = 360.

You could also have calculated the sum of a, b, and c by first finding their values.

Because 2 of the interior angles total 124 (43 + 81), the third angle must measure 180 − 124 = 56. Therefore, angle c must measure 180 − 56 = 124, angle a must measure 180−43 = 137, and angle b must measure 180−81 = 99.

The sum is 137 + 99 + 124 = 360.

If Tom traveled 45 miles in 12 hours and Jim traveled four times as far in one-third the time, what was Jim’s average speed, in miles per hour?

A. 5
B. 15
C. 30
D. 45
E. 90

Solution

You are given that Tom traveled 45 miles in 12 hours and that Jim traveled four times as far in one-third the time.

That means that Jim traveled 45 × 4, or 180 miles in 12×(¹⁄₃), or4 hours.

Therefore, Jim traveled \(\frac{180}{4}\) , or 45 miles per hour.

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