# SAT Practice Test 5, Section 9: Questions 6 - 10

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.

Given:

To find:

Solution:

Given:
a2 – b2 = 7, a and b are positive integers

To find:
The value of a

Solution:
Topic(s): Difference of two squares, addition method

a2 – b2 = 7 ⇒ (a – b)(a + b) = 7 (Difference of two squares)

7 have only 2 factors: 1 and 7.

Given a and b are positive integers
So, a – b = 1 (equation 1)
a + b = 7 (equation 2)

Using the addition method for equation 1 and equation 2, we get
2a = 8 ⇒ a = 4

Given:
The number line

To find:
The point that corresponds to

Solution:
Topic(s): Absolute value

is the length of the line segment from u to w.

From the number line, the nearest estimate to that length is the value x.

Given:
A number n is increased by 5
The result is multiplied by 5
It is then decreased by 5
Finally, it is divided by 5

To find:
The final result in terms of n

Solution:
Topic(s): Translating words to equations

Given:
Philip starts with a 300-foot roll of masking tape
He uses 4 piece of masking tape, each 6 inches long, to put up each poster.
He puts up n posters

To find:
The number of feet of masking tape left on the roll

Solution:
Topic(s): Translating words to equations

To put up one poster, he needs 4 × 6 = 24 inches = 2 ft of tape
For n posters, he needs 2n ft. of tape
Tape left on the roll after he had put up n posters would be 300 – 2n

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