 # SAT Practice Test 5, Section 3: Questions 11 - 15

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.

Given:
Twice a number decreased by 3 is 253

To find:
The number

Solution:
Topic(s): Translating words to equations

Let n be the number Given:
A company manufactures white and black sneakers, both of which are available either high-tops or low-tops

To find:
The number of black sneakers manufactured by the company

Solution:

 High-Tops Low-tops Total White 3,600 Black 900 1,500 2,400 Total 4,500 5,500 10,000

We need to get is BlackTotal.

TotalHightops = Total – TotalLowtops = 10,000 – 5,500 = 4,500
BlackHighTops = TotalHighTops – WhiteHighTops = 4,500 – 3,600 = 900
BlackTotal = 900 + 1,500 = 2,400

Given:
The figure
PQRS is a rectangle
Points Q and R lie on the graph y = ax2, where a is a constant
Perimeter of PQRS = 10

To find:
The value of a

Solution:
From the diagram, length of PS = QR = 2

Let the length of PQ = RS = r
Perimeter PQRS = 2 + 2 + r + r = 10

⇒ 4 + 2r =10 ⇒2r =6 ⇒ r = 3

The coordinates of R would be (1,3).

Given that R is on the graph y = ax2, we can substitute x = 1 and y = 3 into the equation.
3 = a(1) 2 ⇒ a = 3

14. Correct answer: 8/3, 2.66, 2.67

Given:
ab + b = a + 2c
a = 2 and c = 3

To find:
The value of b

Solution:
Topic(s): Isolate variable Answer: 15. Correct answer: 45/2 < x < 55/2

Given:
The figure l bisects 45 < y < 55

To find:
One possible value for x

Solution:
Topic(s): Corresponding angles, vertical angles Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  