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: 1, 11

Given: A, B, C, D and E, lie on a line, not necessarily in that order AB = 24

Point C is the midpoint of

Point D is the midpoint of

DE = 5

To find: AE

Solution:
Sketch the approximate locations of the points on the line

AB = 24

C is the midpoint of , so AC = 12

D is the midpoint of , so AD = 6

There are two possible positions for E.
If E is between A and D then AE = 6 – 5 = 1
If E is between D and C then AE = 6 + 5 = 11

Answer: Either 1 or 11

12. Correct answer: 39

Given:
Sum of 5 consecutive integers = 185

To find:
The greatest of the 5 consecutive integers

Solution: Topic(s): Consecutive integer problems

Let n be the greatest integer

n – 4 + n – 3 + n – 2 + n – 1 + n = 185
⇒ 5 n – 10 = 185 ⇒ 5n = 195 ⇒ n = 39

Answer: 39

13. Correct answer: 6500

Given:
Gross pay = $1,200 + 20% of the dollar amount of sales
Gross pay = $2,500

To find:
Dollar amount of sales

Solution: Topic(s): Percent

The gross pay is given as $2,500

Let x = Dollar amount of sales
1,200 + 20% x x = 2,500 ⇒ 0.2x = 1,300 ⇒ x = 6,500

Answer: 6500

14. Correct answer: 5/18, .277, .278

Given:
Each wedge makes a 40% angle at the center of the disk
The weight of the uncut disk is 2.5 grams

To find:
The weight of each wedge

Solution: Topic(s): Proportional word problem

The proportion of the weight should be the same as the proportion of the angle of the wedge to the full circle.

If 360º then 2.5 grams if 40º then how many grams?

360 → 2.5

40 →

Answer: 5/18, .277, .278

15. Correct answer: 2

Given: x^{2} − y^{2} = 10 x + y = 5

To find: x – y

Solution: Topic(s): Difference of two squares

Use the difference of two squares to factorize

Answer: 2

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