# SAT Practice Test 7, Section 5: Questions 11 - 15

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.

To find:
The radius of a circle with circumference π

Solution:
Topic(s): Circumference of circle

The formula for circumference of circle is C = 2πr

Given:
4x = 6u = 5v = 7w > 0

To find:
The true statement

Solution:
The variable with the greater coefficient would have the smaller value.

Reorder the equation with the larger coefficients first.
7w = 6u = 5v = 4x

The size of the variables will then be
w < u < v < x

Answer: (D) w < u < v < x

Given:
h(t) = 2(t3 − 3)
h(t) = −60

To find:
2 − 3t

Solution:
2(t3 − 3) = −60
2t3 − 6 = −60
2t3= −54
t3 = −27
t = −3

Substitute t = −3 into 2 − 3t
2 − 3t = 2 −3(−3) = 2 + 9 = 11

Given:
x is divisible by 3
y is divisible by 5

To find:
Which of the following must be divisible by 15

Solution:
If x is divisible by 3, then there exists an integer a where x = 3a
If y is divisible by 5, then there exists an integer b where y = 5b

I. xy = 3a × 5b = 15ab (definitely divisible by 15)

II. 3x + 5y = 3(3a) + 5(5b) = 9a + 25b (not necessarily divisible by 15)

III. 5x + 3y = 5(3a) + 3(5b) = 15a + 15b = 15(a + b) (definitely divisible by 15)

Answer: (D) I and III only

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