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.
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 hightops or lowtops
To find:
The number of black sneakers manufactured by the company
Solution:
HighTops 
Lowtops 
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 = ax^{2}, 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 = ax^{2}, 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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