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

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

 

 

 

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