SAT Practice Test 7, Section 5: Questions 16 - 20

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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.

16. Correct answer: (E)

Given:
The figure

To find:
y + z

Solution:
Topic(s): Supplementary angles

a = 180 –115 = 65 (supplementary angles)

z = 65 + b (exterior angle of a triangle = sum of opposite interior angles)

b = 180 – y (supplementary angles)

z = 65 + 180 – y
y + z = 180 + 65 = 245

Answer: (E) 245

17. Correct answer: (D)

Given:
The sum of 3 consecutive odd integers = 111
n is the least of the 3 integers

To find:
The equation for n

Solution:
Topic(s): Consecutive integer problems

n + n + 2 + n + 4 = 111
3n + 6 = 111

Answer: (D) 3n + 6 = 111

18. Correct answer: (A)

Given:
The figure, which shows part of a circle whose circumference is 45

The arc of length 2 and length b continue to alternate around the entire circle so that there are 18 arcs of each length

To find:
The degree measure of each of the arcs of length b

Solution:
Topic(s): Arc of circle, proportional word problem

18 arcs of each length 2 and b = 45

The length of the arc is proportional to the degree measure.

If 45 then 360º, if then how many degrees?

Answer: (A) 4º

19. Correct answer: (C)

Given:
The cost of maintenance increases by 10% each year
Andrew paid $300 for maintenance this year
The cost c for maintenance on Andrew’s automobile n years from now is given by the function: c(n) = 300xⁿ

To find:
The value of x

Solution:
After one year, Andrew would need to pay
300 + 10% × 300
= 300 + 300(0.1)
= 300(1 + 0.1)
= 300(1.1)

After two years, Andrew would need to pay
300(1.1) + 10% × 300(1.1)
= 300(1.1) + 300(1.1)(0.1)
= 300(1.1)(1 + 1.0)
= 300 (1.1)(1.1)
= 300(1.1)²

After n years, Andrew would need to pay
300(1.1)ⁿ

Equating with the given function:
c(n) = 300xⁿ = 300(1.1)ⁿ
Therefore, x = 1.1

Answer: (C) 1.1

20. Correct answer: (B)

Given:
The figure
The 5 line segments are congruent

To find:
The ratio of the length of to the length of

Solution:
Topic(s): Rhombus, Pythagorean theorem

AB = BC = CD = AD =BD (The 5 line segments are congruent)

This implies that ABCD is a rhombus.