ATB - Ability to Benefit Quantitative Reasoning and Algebra Questions and Answers — 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?
- 2x + 4
- 3x + 2
- 6x + 4 (Correct answer)
- 2x^2 - x - 15
Correct answer: 6x + 4
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'?
- C = 200 - 15p
- C = 200p + 15
- C = (200 + 15)p
- C = 15p + 200 (Correct answer)
Correct answer: C = 15p + 200
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
- x > 7
- x < 7 (Correct answer)
- x < 3
- x > 3
Correct answer: x < 7
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?
- 80
- 400
- 144 (Correct answer)
- 240
Correct answer: 144
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?
- √49
- √12 (Correct answer)
- 0.75
- 9/2
Correct answer: √12
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.
Question 6: A cell phone plan costs $30 per month and includes 2 gigabytes (GB) of data. Each additional gigabyte of data costs $8. If a customer's bill was $54 for one month, how many additional gigabytes of data did they use?
- 2 GB
- 3 GB (Correct answer)
- 4 GB
- 7 GB
Correct answer: 3 GB
First, subtract the base monthly cost from the total bill to find the cost of the additional data: $54 - $30 = $24. Then, divide this amount by the cost per additional gigabyte: $24 / $8 per GB = 3 GB. The customer used 3 additional gigabytes of data.
ATB - Ability to Benefit Quantitative Reasoning and Algebra Questions and Answers
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?