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SAT Practice Test 5, Section 3: 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: 128

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

Answer: 128

12. Correct answer: 2,400

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

Answer: 2,400

13. Correct answer: 3

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

Answer: 3

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

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