SAT Practice Test 7, Section 2: Questions 16 - 18

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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: 71

Given:
Average of 5 positive integers = 15

To find:
The greatest possible integer

Solution:
Topic(s): Statistics

Let t, u, v, w and x be the five positive integers.

In order for x to be the greatest possible integer, t, u, v and w must be the smallest positive integer, which is 1.

1 + 1 + 1 + 1 + x = 75
x = 71

Answer: 71

17. Correct answer: 10/7, 1.42, 1.43

Given:
Alice and Corrine stand back-to-back
They each take 10 steps in opposite directions away from each other and stop
Alice turns around, walks toward Corrine, and reaches her in 17 steps

To find:
The number of times the length of one of Corrine’s steps compared with the length of one of Alice’s steps

Solution:
Topic(s): Integer word problem

Let a be the length of Alice’s steps
Let c be the length of Corrine’s steps

After walking 10 steps each, the girls will be 10a + 10c apart.

When Alice walked back she took 17 steps.

So,

Answer: 10/7

18. Correct answer: 3

Given:
f(x) = x² + 18
f(2m) = 2f(m), for m a positive number

To find:
The value of m

Solution:
f(x) = x² + 18
f(2m) = 2f(m)
(2m²) + 18 = 2(m² + 18)
4m² + 18 = 2m² + 36
2m² = 18
m² = 9
m = 3

Answer: 3