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SAT Practice Test 7, Section 2: Questions 11 - 15

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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.

11. Correct answer: 875


for all positive integers x, y and z

To find:
The value of


103 − 53
= 1000 − 125
= 875

Answer: 875

12. Correct answer: 2, 3

The figure
PQST is a rectangle
URST is a square
PU = 5
UT is a positive number
Area of PQST must be more than 10 but less than 30

To find:
One possible value of UT

Topic(s): Area of rectangle

Let x = UT
10 < area of PQST < 30
10 < x(x + 5) < 30

We need to find one integer value for x that will fit the range.

For example
Let x = 2.
x(x + 5)
= 2( 2 + 5)

x can also be 3
Let x = 3.
x(x + 5)
= 3( 3 + 5)

Answer: 2 or 3

13. Correct answer: 36

of the balloons are red
There are half as many green balloons, as there are red balloons
There are 18 blue balloons

To find:
The number of balloons

Let x = number of balloons in the box

Answer: 36

14. Correct answer: 12

Points P, Q and R lie on a line l
Points S, T, U and V lie on a different line that is parallel to line l

To find:
The total number of different lines that can be drawn so that each line contains exactly 2 of the 7 points

In order to draw the line, we need one point from P, Q or R and another point from S, T, U or V.
The total number of possible selections would be 3 × 4 = 12

Answer: 12

15. Correct answer: 5

2x + 2x + 2 x+ 2x = 27

To find:
The value of x

Topic(s): Exponents

(Be careful, we can only add the exponents when we are multiplying bases that are equal)

Answer: 5


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