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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.

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: 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 10*a* + 10*c* apart.

When Alice walked back she took 17 steps.

So,

**Answer: 10/7**

**18. Correct answer: 3**

Given:

*f*(*x*) = *x*^{2} + 18

*f*(2*m*) = 2*f*(*m*), for *m* a positive number

To find:

The value of *m*

Solution:

*f*(*x*) = *x*^{2} + 18

*f*(2*m*) = 2*f*(*m*)

(2*m*^{2}) + 18 = 2(*m*^{2} + 18)

4*m*^{2} + 18 = 2*m*^{2} + 36

2*m*^{2} = 18

*m*^{2} = 9

*m* = 3

**Answer: 3**

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