SAT Practice Test 2, Section 6: Questions 16  18
The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the Official SAT Study Guide.
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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 90minute 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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