ATB - Ability to Benefit Quantitative Reasoning and Algebra Questions and Answers

Question 1

A rectangular garden has a length of (2x + 5) meters and a width of (x - 3) meters. Which of the following expressions represents the perimeter of the garden in meters?

Accepted Answer

6x + 4

Answer

The formula for the perimeter of a rectangle is P = 2(length + width). Substitute the given expressions: P = 2((2x + 5) + (x - 3)). First, combine the like terms inside the parentheses: (2x + x) + (5 - 3) = 3x + 2. Then, distribute the 2: P = 2(3x + 2) = 6x + 4.

Question 2

A local community center is organizing a trip. A bus can be rented for a flat fee of $200, plus an additional $15 for each person who attends. If 'p' represents the number of people attending, which equation correctly models the total cost 'C'?

Accepted Answer

C = 15p + 200

Answer

The total cost (C) is the sum of the fixed flat fee and the variable cost per person. The flat fee is a constant $200. The cost per person is $15 multiplied by the number of people (p), which is 15p. Therefore, the correct equation is C = 15p + 200.

Question 3

Solve the following inequality for x: 3x - 7 < 14

Accepted Answer

x < 7

Answer

To solve the inequality 3x - 7 < 14, first add 7 to both sides: 3x < 14 + 7, which simplifies to 3x < 21. Next, divide both sides by 3: x < 21 / 3. This gives the final answer, x < 7.

Question 4

The ratio of cars to parking spots in a garage is 3 to 5. If the garage has a total of 240 parking spots, how many cars are currently in the garage?

Accepted Answer

144

Answer

The ratio 3 to 5 can be written as the fraction 3/5. Set up a proportion: 3/5 = x/240, where x is the number of cars. To solve for x, cross-multiply: 5 * x = 3 * 240. This gives 5x = 720. Divide both sides by 5: x = 144. So, there are 144 cars in the garage.

Question 5

Which of the following is an example of an irrational number?

Accepted Answer

√12

Answer

An irrational number cannot be expressed as a simple fraction, and its decimal representation is non-repeating and non-terminating. √49 = 7, 0.75 = 3/4, and 9/2 are all rational numbers. √12 is irrational because 12 is not a perfect square, and its decimal form (approximately 3.4641...) goes on forever without repeating.

ATB - Ability to Benefit Practice Test

ATB - Ability to Benefit Practice Test

ATB - Ability to Benefit Quantitative Reasoning and Algebra Questions and Answers