NTS - National Testing Service Quantitative Reasoning: Algebra Questions and Answers

Question 1

If 3x - 7 = 5x + 1, what is the value of 2x + 9?

Accepted Answer

1

Answer

First, solve for x in the equation 3x - 7 = 5x + 1. Subtract 3x from both sides to get -7 = 2x + 1. Then, subtract 1 from both sides to get -8 = 2x. Divide by 2 to find x = -4. Now, substitute the value of x into the expression 2x + 9. This gives 2(-4) + 9, which simplifies to -8 + 9 = 1.

Question 2

A rectangle's length is 5 cm more than its width. If the perimeter of the rectangle is 50 cm, what is the area of the rectangle in square cm?

Accepted Answer

150

Answer

Let the width be 'w'. Then the length 'l' is w + 5. The perimeter of a rectangle is 2(l + w). So, 2((w + 5) + w) = 50. Simplifying gives 2(2w + 5) = 50, which leads to 4w + 10 = 50. Solving for w, we get 4w = 40, so w = 10 cm. The length is w + 5 = 10 + 5 = 15 cm. The area is length × width, which is 15 cm × 10 cm = 150 square cm.

Question 3

If a/b = 4 and a - 2b = 10, which of the following is the value of 'a'?

Accepted Answer

20

Answer

From the first equation, a/b = 4, we can express 'a' in terms of 'b': a = 4b. Now, substitute this expression into the second equation: (4b) - 2b = 10. This simplifies to 2b = 10, so b = 5. To find 'a', substitute the value of 'b' back into a = 4b. This gives a = 4(5), so a = 20.

Question 4

In a school, the ratio of boys to girls is 3:5. If there are a total of 720 students, how many more girls are there than boys?

Accepted Answer

180

Answer

The ratio 3:5 means there are 3+5 = 8 parts in total. To find the value of one part, divide the total number of students by the total number of parts: 720 / 8 = 90 students per part. The number of boys is 3 parts × 90 = 270. The number of girls is 5 parts × 90 = 450. The difference is 450 - 270 = 180.

Question 5

If x² - y² = 48 and x - y = 4, what is the value of x + y?

Accepted Answer

12

Answer

The expression x² - y² is a difference of squares, which can be factored into (x - y)(x + y). We are given that x² - y² = 48 and x - y = 4. So, we can substitute these values into the factored equation: 4 * (x + y) = 48. To solve for (x + y), divide both sides by 4: (x + y) = 48 / 4 = 12.

NTS - National Testing Service Practice Test

NTS - National Testing Service Practice Test

NTS - National Testing Service Quantitative Reasoning: Algebra Questions and Answers