 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

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

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

Given:
4(x + y)(xy) = 40 (equation 1)
xy = 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: Given:
The center of the circle has coordinates (5, 12)
The circle touches the x-axis at one point only.

To find:

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 Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 