SAT Practice Test 4, Section 4: Questions 11 - 15

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)

To find:
x + y.

Solution:
Topic(s): Substitution

Substitute equation 2 into equation 1
4(x + y) × 20 = 40
4(x + y) = 2

(x + y) =

Answer:

15. Correct answer: 12

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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