# 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.

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:

Substitute x = 2m

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

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.

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

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