# SAT Practice Test 8, Section 2: Questions 6 - 10

This is for SAT in Jan 2016 or before.

The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the The Official SAT Study Guide Second Edition.

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:
4 consecutive positive integers are divided by 3

To find:
The remainders

Solution:
If a positive integer is divided by 3, then its remainder would be in the range of 0 to 2 inclusive.

If 4 consecutive positive integers were each divided by 3, then the remainders could be 0, 1, 2, 0

Answer: (D) 0, 1, 2, 0

Given:
y is inversely proportional to x
y = 15 when x = 5

To find:
The value of y when x = 25

Solution:
Topic(s): Inversely proportional

If y is inversely proportional to x then xy is a constant.

Given:
2x + z = 2y
2x + 2y + z = 20

To find:
The value of y

Solution:
Topic(s): Substitution

2x + z = 2y (equation 1)
Rewrite 2x + 2y + z = 20 as 2x + z + 2y = 20 (equation 2)

Substitute equation 1 into equation 2
2y + 2y = 20
4y = 20
y = 5

Given:
2(x − 3) = 7

To find:
The value of x

Solution:
Topic(s): Isolate variable

Given:
Point P lies on the line with equation y − 4 = 3(x − 2)
x-coordinate of P is 4

To find:
The y-coordinate of P

Solution:
Topic(s): Substitution

y − 4 = 3(x − 2)

Substitute x = 4 to find y
y − 4 = 3(4 − 2)
y = 6 + 4 = 10