SAT Practice Test 6, Section 9: 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.

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11. Correct answer: (C)

Given:
The table

To find:
Car engine oil with a rating of 5W is how many times as fast as car engine oil with rating of 20W

Solution:
From the table;

5W = 2 × 10W
10W = 2 × 15W
15W = 2 × 20W

This means that
5W = 2 × 10W
= 2 × 2 × 15W
= 2 × 2 × 2 × 20W
= 8 × 20W

Answer: (C) 8

12. Correct answer: (E)

Given:
The figure
Points P, A and B are equally spaced on line l
Points P, Q and R are equally spaced on line m

PB = 4
PR = 6
AQ = 4

To find:
Perimeter of QABR

Solution:
Topic(s): RAR rule

Triangles PAQ and PBR are similar triangles (RAR)

The ratio of the sides is the same.

The perimeter of the quadrilateral QABR = 4 + 2 + 3 + 8 = 17

Answer: (E) 17

13. Correct answer: (D)

Given:
g(n) = n² + n
h(n) = n² − n

To find:
g(5) - h(4)

Solution:
g(5) = 52 + 5 = 30
h(4) = 42 − 4 = 12
g(5) − h(4) = 30 −12 = 18

Answer; (D) 18

14. Correct answer: (A)

Given:
g(n) = n² + n
h(n) = n² − n

To find:
h(m + 1)

Solution:
h(m + 1)
= (m + 1)² − (m + 1)
= m² + 2m + 1 − m − 1
= m² + m
= g(m)

Answer: (A) g(m)

15. Correct answer: (B)

Given:
The selling price of a sweater = $28
The selling price is 40% more than the cost price
Employees can purchase the sweater at 30% off the cost price

To find:
The amount the employees pay for the sweater

Solution:
Topic(s): Percent

Let c be the cost price of the sweater.
c + 40% × c = 28
c + 0.4c = 28
1.4c = 28
c = 20

Purchase price = 20 − 30% × 20
= 20 − 0.3 × 20
= 20 − 6
= 14

Answer: (B) $14.00

16. Correct answer: (C)

Given:
A rectangle ABCD
Point E is the midpoint of
Area of ABED is

To find:
Area of ABCD

Solution:
Topic(s): Area of trapezium

Let AB = l and BE = w

Area of trapezium ABED =

Area of rectangle ABCD =

Correct answer: (C)

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