SAT Practice Test 5, Section 7: 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.

11. Correct answer: (C)

Given:
x³ = y⁹

To find:
x in terms of y

Solution:
Topic(s): Exponents

Answer: (C) y³

12. Correct answer: (E)

Given:
The figure

To find:
The line segment with slope of -1

Solution:
Topic(s): Coordinate geometry

A negative slope would mean the line is slanting from left to right.

13. Correct answer: (A)

Given:
The combination consists of 3 two-digit numbers
The combination satisfies

• One number is odd
• One number is a multiple of 5
• One number is the day of the month of Kyle's birthday

If each number satisfies exactly one of the conditions, which of the following could be the combination of the lock?

To find:
The combination to the lock

Solution:
Test out the answers. Valid day of month should be between 1 and 31 (inclusive). Make sure that each of the number satisfies exactly one of the conditions.

(A) 14-20-13

This can be obtained by elimination.

(B)14-25-13 is incorrect because 25 is a multiple of 5 and it is odd
(C) 15-18-16 is incorrect because 15 is a multiple of 5 and it is odd
(D) 20-15-20 is incorrect because 15 is a multiple of 5 and it is odd
(E) 34-30-21 is incorrect because 21 is odd, 30 is a multiple of 5, but 34 is not a valid day.

Only (A) could be correct.
20 is a multiple of 4, 13 is odd and Kyle's birthday is on the 14

Answer: (A) 14-20-13

14. Correct answer: (C)

Given:
x > 3

To find:
An equation equivalent to

Solution:

Square both sides
x + 9 = (x - 3)² ⇒ x + 9 = x² – 6x + 9 ⇒ x = x² – 6x

Answer: (C) x = x² – 6x

15. Correct answer: (E)

To find:
The number of integers from 1 to 100, inclusive that are not the square of an integer

Solution:
Topic(s): Squares of integers

Square of integers from 1 to 100
1² = 1, 2² = 4, 3² = 9, …, 10² = 100

There are 10 integers from 1 to 100 that are squares.

So there are 100 – 10 = 90 integers that are not squares.

Answer: (E) 90

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