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: 8, 10 or 12

Given:
When the positive even integer n is increased by 50% of itself, the result is between 10 and 20:

To find:
One possible value of n

Solution: Topic(s): Percent

10 < n + 50%n < 20
10 < n + 0.5n < 20
10 < 1.5n < 20
6.67 < n < 13.33

Remember, n is an even integer.

The possible even integers in the required range, 6.67 < n < 13.33, would be 8, 10 and 12

Answer: Any one of following: 8, 10 or 12

12. Correct answer: 3400

Given:
The perimeter of the rectangle is 250.
The length of one side is 40.

To find:
Area of the rectangle

Solution: Topic(s): Area and perimeter of rectangle

First, we need to find the length of the other side of the rectangle.
Formula of perimeter of rectangle: 2(l + w)
Substitute in the given values:

2(40 + w) = 250
80 + 2w = 250
2w = 170 w = 85

Next, we calculate the area
Formula for area of rectangle: lw lw = 40 × 85 = 3400

Answer: 3400

13. Correct answer: 450

Given:
A school ordered $600 worth of light bulbs
Some bulbs cost $1 each
Some bulbs cost $2 each
There are twice as many $1 bulbs as $2 bulbs

To find:
The number of light bulbs ordered altogether

Solution: Topic(s): Integer word problem

Let b be the number of $2 light bulbs ordered
2b be the number of $1 light bulbs ordered

Altogether, the school ordered $600 worth of light bulbs. b × 2 + 2b × 1 = 600
2b + 2b = 600
4b = 600 b = 150

Total number of bulbs = b + 2b = 3b = 3 × 150 = 450

Answer: 450

14. Correct answer: 1/2

Given:
4(x + y)(x – y) = 40 (equation 1) x – y = 20 (equation 2)

Given:
The center of the circle has coordinates (5, 12)
The circle touches the x-axis at one point only.

To find:
The radius of the circle.

Solution: Topic(s): Tangent of circle

First, we can sketch the diagram.

For the circle to touch the x-axis at only one point, the x-axis must be a tangent to the circle. A tangent is perpendicular to the radius at the point of contact. So the radius must be 12

Answer: 12

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