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Free Quantitative Reasoning MCQs with Answers

625 Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.

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625 questions · page 12 of 32

221. The table shown summarizes the number of employees at each of the 17 restaurants in a town. Which of the following could be the median number of employees for the restaurants in this town?

  • A. 2
  • B. 9
  • C. 15
  • D. 21

Explanation: Choice D is correct. If a data set contains an odd number of data values, the median is represented by the middle data value in the list…

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Correct answer: 21

222. The right triangle ABC is shown. What is the value of tan A?

  • A. √3/54
  • B. 1/√3
  • C. √3
  • D. 27√3

Explanation: Choice C is correct. In the triangle shown, the measure of angle B is 30° and angle C is a right angle, which means that it has a measure…

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Correct answer: √3

223. At the time that an article was first featured on the home page of a news website, there were 40 comments on the article. An exponential model estimates that at the end of each hour after the article was first featured on the home page, the number of comments on the article had increased by 190% of the number of comments on the article at the end of the previous hour. Which of the following equations best represents this model, where C is the estimated number of comments on the article t hours after the article was first featured on the home page and t ≤ 4?

  • A. C = 40(1.19)t
  • B. C = 40(1.9)t
  • C. C = 40(19)t
  • D. C = 40(2.9)t

Explanation: Choice D is correct. It's given that an exponential model estimates that the number of comments on an article increases by a fixed…

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Correct answer: C = 40(2.9)t

224. In right triangle ABC, angle C is the right angle, and BC = 162. Point D on side AB is connected by a line segment with point E on side AC such that line segment DE is parallel to side BC and CE = 2AE. What is the length of line segment DE?

  • A. 50
  • B. 48
  • C. 54
  • D. 60

Explanation: The correct answer is 54. To solve this problem, recognize that triangle ADE is similar to triangle ABC because DE is parallel to BC…

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Correct answer: 54

225. The graph of function f is shown, where y = f(x).Which of the following describes function f?

  • A. Increasing linear
  • B. Decreasing linear
  • C. Increasing exponential
  • D. Decreasing exponential

Explanation: Choice A is correct. The graph of function f shows that as x increases, f(x) also increases, which means f(x) is an increasing function.

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Correct answer: Increasing linear

226. The graph of the function f is shown, where y = f(x) What is the y-intercept of the graph?

  • A. (0, −1)
  • B. (0, −4)
  • C. (0, 1)
  • D. (0, 4)

Explanation: Choice B is correct. The y-intercept of a graph is the point where the graph intersects the y-axis.

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Correct answer: (0, −4)

227. The function f defined by f (t) = 14t + 9 gives the estimated length, in inches, of a vine plant t months after Tavon purchased it. Which of the following is the best interpretation of 9 in this context?

  • A. Tavon will keep the vine plant for 9 months.
  • B. The vine plant is expected to grow 9 inches each month.
  • C. The vine plant is expected to grow to a maximum length of 9 inches.
  • D. The estimated length of the vine plant was 9 inches when Tavon purchased it.

Explanation: Choice D is correct. It's given that the function f defined by f (t) = 14t + 9 gives the estimated length, in inches, of a vine plant t…

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Correct answer: The estimated length of the vine plant was 9 inches when Tavon purchased it.

228. A rectangle has an area of 155 square inches. The length of the rectangle is 4 inches less than 7 times the width of the rectangle. What is the width of the rectangle, in inches?

  • A. 5
  • B. 8
  • C. 10
  • D. 15

Explanation: The correct answer is 5. Let x represent the width of the rectangle. The length is 7x - 4. The area is calculated as x(7x - 4) = 155.

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Correct answer: 5

229. 4, 10, 18, 4, 4, 5, 6, 5 What is the median of the data set shown?

  • A. 4
  • B. 5
  • C. 7
  • D. 14

Explanation: Choice B is correct. If a data set contains an even number of data values, when the data values are listed in ascending or descending…

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Correct answer: 5

230. A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is 24 square centimeters. What is the height, in centimeters, of the cylinder?

  • A. 18
  • B. 24
  • C. 216
  • D. 10,368

Explanation: Choice A is correct. The volume V of a right circular cylinder is calculated using the formula V = πr^2h, where πr^2 is the area of the…

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Correct answer: 18

231. The table shows the linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. Which equation represents the linear relationship between c and p?

  • A. 55c − p = −9
  • B. 55c − p = 9
  • C. 55p - c = -9
  • D. 55p - c = 9

Explanation: Choice A is correct. It's given that there is a linear relationship between the number of cars, c, on a commuter train and the maximum…

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Correct answer: 55c − p = −9

232. If 48c = 3√47, what is the value of c?

  • A. 7/20
  • B. 7/10
  • C. 7/15
  • D. 7/24

Explanation: The correct answer is 7/24. Begin by expressing the cube root as a fractional exponent: 3√47 becomes 47/3.

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Correct answer: 7/24

233. (x - 2) - 4 (y + 7) = 117(x - 2) + 4 (y + 7) = 442The solution to the given system of equations is (x, y). What is the value of 6(x - 2)?

  • A. 1,660
  • B. 1,665
  • C. 1,677
  • D. 1,680

Explanation: To find the value of 6(x - 2), first, notice that adding the two equations together helps eliminate the y terms.

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Correct answer: 1,677

234. In triangle ABC, angle B is a right angle. The length of side AB is 10√37 and the length of side BC is 24√37. What is the length of the side AC?

  • A. 14√37
  • B. 26√37
  • C. 34√37
  • D. √(34.37)

Explanation: Choice B is correct. The Pythagorean theorem states that for a right triangle, c2 = a2 + b2, where c represents the length of the…

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Correct answer: 26√37

235. x = y - 3x/2 + 2y = 6Which ordered pair (x, y) satisfies the system of equations shown above?

  • A. (-3, 0)
  • B. (0, 3)
  • C. (6, -3)
  • D. (36, -6)

Explanation: Choice B is correct. The first equation can be rewritten as y - x = 3 and the second as x/4 + y = 3, which implies that -x = x/4 and so x…

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Correct answer: (0, 3)

236. If f(x) = x2 - 6x + 3 / x - 1, what is f (-1)?

  • A. -5
  • B. -2
  • C. 2
  • D. 5

Explanation: Choice A is correct. To find f(-1), substitute -1 into the function: f(x) = x2 - 6x + 3 / x - 1.

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Correct answer: -5

237. Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

  • A. 640x + 880y ≥ 9,700x + y ≤ 10x ≥ 3y ≥ 1
  • B. 640x + 880y ≤ 9,700x + y ≥ 10x ≥ 3y ≥ 1
  • C. 640x + 880y ≥ 9,700x + y ≥ 10x ≤ 3y ≤ 1
  • D. 640x + 880y ≤ 9,700x + y ≤ 10x ≤ 3y ≤ 1

Explanation: The correct answer is Option B. It correctly captures all the conditions of the problem.

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Correct answer: 640x + 880y ≤ 9,700x + y ≥ 10x ≥ 3y ≥ 1

238. A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?

  • A. 0 < x ≤ 10
  • B. 0 < x ≤ 11 (2/3)
  • C. 0 < x ≤ 17 (1/2)
  • D. 0 < x ≤ 20

Explanation: Choice A is correct because the perimeter of the base is calculated as 7x inches, and the height is 60 inches.

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Correct answer: 0 < x ≤ 10

239. The expression 1/3x2 - 2 can be rewritten as 1/3 (x - k)(x + k), where k is a positive constant. What is the value of k?

  • A. 2
  • B. 6
  • C. √2
  • D. √6

Explanation: Choice D is correct. Start by factoring the expression: 1/3 (x2 − 6). Recognize that x2 − 6 is a difference of squares, allowing it to be…

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Correct answer: √6

240. The number of radians in a 720-degree angle can be written as aπ, where a is a constant. What is the value of a?

  • A. 3
  • B. 4
  • C. 5
  • D. 6

Explanation: The correct answer is 4. To convert degrees to radians, use the formula: Radians = Degrees × (π/180).

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Correct answer: 4
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