The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the Official SAT Study Guide.

It would be best that you go through the SAT practice test questions in the Study Guide first and then look at the worked solutions for the questions that you might need assistance in. Due to copyright issues, we are not able to reproduce the questions, but we hope that the worked solutions will be helpful.

16. Correct answer: Either 2 or 7

Given:

h(2m) = 9m

To find:
The value of m

Solution: Topic(s): Factoring quadratic equations

Substitute x = 2m

Factorize the quadratic equation.

Find the factors of 14 whose sum is –9:

–1 + (–14) ≠ –9
–2 + (–7) = –9 ü
(m – 2)(m – 7) = 0 m = 2 or m = 7

Answer: Either 2 or 7

17. Correct answer: 149

Given:
A table indicating the clocks and their frequency of chimes

To find:
Total number of chimes in the 90-minute period from 7:15 to 8:45

Solution:
From 7:15 to 8:45, the clocks may chime at these times; 7:30, 8:00 and 8:30.

No. of chimes

Total chimes for one clock

No. of clocks

Total chimes for each type

Time

7:30

8:00

8:30

Type A

1

8

1

10

10

10 × 10 = 100

Type B

8

8

5

8 × 5 = 40

Type C

1

1

1

3

3

3× 3 = 9

Total number of chimes = 100 + 40 + 9 = 149.

Answer: 149

18. Correct answer: 72

Given:
Five cards are placed in a row
The shaded card is never placed at either end

To find:
The number of different arrangements

Solution: Topic(s): Permutations

The shaded card cannot be at either end so it can be at 3 positions i.e. positions B, C or D.

The second card can be placed at 4 other positions.
The third card can be placed at 3 other positions.
The fourth card can be placed at 2 other positions.
The fifth card can be placed at 1 position. (Permutations)

The number of different arrangements possible is

3 × 4 × 3 × 2 × 1 = 72

Answer: 72

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