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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 17 of 32

321. A small business owner budgets $2,200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and$11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

  • A. 182
  • B. 4.9
  • C. 7
  • D. 9

Explanation: The correct answer is 182. Let s represent the number of small candles the owner can purchase, and let  represent the number of large…

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Correct answer: 182

322. Triangle FGH is similar to triangle JKL, where angle F corresponds to angle J and angles G and K are right angles. If sin (F) = 308 / 317, what is the value of sin ( J ) ?

  • A. 75/317
  • B. 308/317
  • C. 317/308
  • D. 317/75

Explanation: Choice B is correct. If two triangles are similar, then their corresponding angles are congruent.

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Correct answer: 308/317

323. The circle has center O, circumference 144π,and diameters PR and QS. The length of arc PS is twice the length of arc PQ. What is the length of arc QR ?

  • A. 24π
  • B. 48π
  • C. 72π
  • D. 96π

Explanation: Choice B is correct. Since PR and QS are diameters of the circle shown, OS, OR, OP, and OQ are radii of the circle and are therefore…

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Correct answer: 48π

324. A sample of oak has a density of 807 kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.90 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?

  • A. 588
  • B. 726
  • C. 897
  • D. 1,107

Explanation: To find the mass of the cube, calculate the volume first by cubing the edge length to get 0.729 cubic meters.

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Correct answer: 588

325. The table shows the results of a poll. A total of 803 voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if 6,424 people vote in the election, by how many votes would Angel Cruz be expected to win?

  • A. 163
  • B. 1,304
  • C. 3,864
  • D. 5,621

Explanation: Choice B is correct. It's given that 483 out of 803 voters responded that they would vote for Angel Cruz.

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Correct answer: 1,304

326. A company that provides whale-watching tours takes groups of 21 people at a time. The company'srevenue is 80 dollars per adult and 60 dollars perchild. If the company's revenue for one group consisting of adults and children was 1,440 dollars,how many people in the group were children?

  • A. 3
  • B. 9
  • C. 12
  • D. 18

Explanation: To solve this problem, let x be the number of adults and y be the number of children. The total number of people is 21, so x + y = 21.

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Correct answer: 12

327. One of the factors of 2x3 + 42x 2 + 208x is x + b, where b is a positive constant. What is the smallest possible value of b ?

  • A. 2
  • B. 4
  • C. 6
  • D. 8

Explanation: The given expression is 2x3 + 42x2 + 208x. First, factor out the common factor of 2x: this gives 2x(x2 + 21x + 104).

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Correct answer: 8

328. y = − 1.5y = x2 + 8x + aIn the given system of equations, a is a positive constant. The system has exactly one distinct real solution. What is the value of a ?

  • A. 6
  • B. 4
  • C. 29/2
  • D. 8

Explanation: The correct answer is 29 /2 . According to the first equation in the given system, the value of y is -1.5.

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Correct answer: 29/2

329. RS = 20ST = 48TR = 52The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW, where S corresponds to V and T corresponds to W. What is the value of tan W ?

  • A. 5/13
  • B. 5/12
  • C. 12/13
  • D. 12/5

Explanation: Choice B is correct. Given that the triangles RST and UVW are similar, angle T corresponds to angle W.

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Correct answer: 5/12

330. One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of w square feet. Which equation represents the total amount of paint P, in gallons, needed to paint the walls of the room twice?

  • A. P = w/110
  • B. P = 440w
  • C. P = w/220
  • D. P = 220w

Explanation: Choice A is correct. The problem specifies that the walls need to be painted twice, covering 2w square feet.

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Correct answer: P = w/110

331. Jay walks at a speed of 3 miles per hour and runs at a speed of 5 miles per hour. He walks for w hours and runs for r hours for a combined total of 14 miles. Which equation represents this situation?

  • A. 3 +5 w r = 14
  • B. 1/3w+ 1/5r =14
  • C. 1/3w=1/5r=112
  • D. 3w + 5r = 112

Explanation: Choice A is correct. Since Jay walks at a speed of 3 miles per hour for w hours,Jay walks a total of 3w miles.

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Correct answer: 3 +5 w r = 14

332. 73, 74, 75, 77, 79, 82, 84, 85, 91What is the median of the data shown?

  • A. m6q8z-1
  • B. m5q9z2
  • C. 79
  • D. m20q12z-2

Explanation: The correct answer is 79. The median of a data set with an odd number of values is the middle value of the set when the values are ordered…

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Correct answer: 79

333. g m = −0.05m + 12.1The given function g models the number of gallons of gasoline that remains from a full gas tank in a ca rafter driving m miles. According to the model, about t how many gallons of gasoline are used to drive each mile?

  • A. 0.05
  • B. 12.1
  • C. 20
  • D. 242.0

Explanation: Option A is correct. The function g(m) = -0.05m + 12.1 models the amount of gasoline remaining in the tank after driving m miles.

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Correct answer: 0.05

334. Triangle XYZ is similar to triangle RST such that X,Y, and Z correspond to R, S, and T, respectively.The measure of ∠Z is 20° and 2 XY = RS. What is the measure of ∠T ?

  • A. 2
  • B. 10
  • C. 20
  • D. 40

Explanation: Choice C is correct. It's given that triangle XYZ is similar to triangle RST , such that X, Y , and Z correspond to R, S, and T…

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Correct answer: 20

335. 5x + 10x + 16 = 0How many distinct real solutions does the given equation have?

  • A. Exactly One
  • B. Exactly Two
  • C. Infinitely many
  • D. Zero

Explanation: Choice D is correct. Simplifying the given equation 5x + 10x + 16 = 0 results in 15x + 16 = 0.

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Correct answer: Zero

336. A certain park has an area of 11,863,808 square yards. What is the area, in square miles, of this park?(1 mile = 1,760 yards)

  • A. 1.96
  • B. 3.83
  • C. 3,444.39
  • D. 6,740.8

Explanation: Choice B is correct. To convert the area from square yards to square miles, we need to understand that 1 mile is equal to 1,760 yards.

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Correct answer: 3.83

337. In triangles ABC and DEF, angles B and E each have measure 27° and angles C and F each have measure 41°. Which additional piece of information is sufficient to determine whether triangle ABC is congruent to triangle DEF ?

  • A. The measure of angle A
  • B. The length of side AB
  • C. The lengths of sides BC and EF
  • D. No additional information is necessary.

Explanation: Choice C is correct. Since angles B and E each have the same measure and angles C and F each have the same measure, triangles ABC and DEF…

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Correct answer: The lengths of sides BC and EF

338. Two data sets of 23 integers each are summarized in the histograms shown. For each of the histograms,the first interval represents the frequency of integers greater than or equal to 10, but less than 20. Thesecond interval represents the frequency of integers greater than or equal to 20, but less than 30, and soon. What is the smallest possible difference between the mean of data set A and the mean of data set B?

  • A. 0
  • B. 1
  • C. 10
  • D. 23

Explanation: The histograms presented show that Data Set A has higher overall values compared to Data Set B.

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Correct answer: 1

339. A right triangle has legs with lengths of 24 centi meters and 21 centi meters. If the length of this triangle's hypotenuse, in centi meters, can be written in the form 3 d, where d is an integer, what is the value of d

  • A. 113
  • B. 1
  • C. 10
  • D. 23

Explanation: .The correct answer is 113. It's given that the legs of a right triangle have lengths 24 centimeters and 21 centimeters.

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Correct answer: 113

340. What percentage of 300 is 75?

  • A. 25%
  • B. 50%
  • C. 75%
  • D. 225%

Explanation: To determine what percentage 75 is of 300, use the formula (part/whole) × 100. Here, the part is 75, and the whole is 300.

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Correct answer: 25%
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