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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 24 of 32

461. Circle A has a radius of 3n and circle B has a radius of 129n, where n is a positive constant. The area of circle B is how many times the area of circle A?

  • A. 43
  • B. 86
  • C. 129
  • D. 1,849

Explanation: Choice D is correct. The area of a circle can be found by using the formula A = πr2 , where A is the area and r is the radius of the…

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Correct answer: 1,849

462. The measure of angle R is 2π / 3 radians. The measure of angle T is 5π / 12 radians greater than the measure ofangle R. What is the measure of angle T, in degrees?

  • A. 75
  • B. 120
  • C. 195
  • D. 390

Explanation: Choice C is correct. It's given that the measure of angle R is 2π3 radians, and the measure of angle T is π5 / 12 radians greater than the…

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Correct answer: 195

463. The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is k 3 centimeters, where k is a constant. What is the value of k?

  • A. 40
  • B. 100
  • C. 104
  • D. 204

Explanation: The correct answer is 104. An equilateral triangle is a triangle in which all three sides have the same length and all three angles have a…

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Correct answer: 104

464. A researcher surveyed a random sample of students from a large university about how often they see movies. Using the sample data, the researcher estimated that 23% of the students in the population saw a movie at least once per month. The margin of error for this estimation is 4%. Which of the following is the most appropriate conclusion about all students at the university, based on the given estimate and margin of error?

  • A. It is unlikely that less than 23% of the students see a movie atleast once per month.
  • B. At least 23%, but no more than 25%, of the students see a movie at least once per month.
  • C. The researcher is between 19% and 27% sure that most students see a movie at least once per month.
  • D. It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%.

Explanation: Choice D is correct. The margin of error is applied to the sample statistic to create an interval in which the population statistic most…

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Correct answer: It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%.

465. A book was on sale for 40% off its original price. If the sale price of the book was $18.00, what was the original price of the book? (Assume there is no sales tax.)

  • A. $7.20
  • B. $10.80
  • C. $30.00
  • D. $45.00

Explanation: Choice C is correct. Let x represent the original price of the book. Then, 40% off of x is (1 − 0.40)x, or 0.60x.

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Correct answer: $30.00

466. The volume of a sphere is given by the formula V = 4/3πr3, where r is the radius of the sphere. Which of the following gives the radius of the sphere in terms of the volume of the sphere?

  • A. 4π/3V
  • B. 3V/4π
  • C. 3√4π/3V
  • D. 3√3V/4π

Explanation: Choice D is correct. Dividing both sides of the equation V = 4/3 πr3 by 4/3π results in 3V/4π = r3.

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Correct answer: 3√3V/4π

467. In quadrilateral ABCD, AD  BC and CD = 1/2 AB. What is the measure of angle B?

  • A. 150°
  • B. 135°
  • C. 120°
  • D. 90°

Explanation: Choice A is correct. A segment can be drawn inside of quadrilateral ABCD from point B to point F (not shown) on segment AD such that…

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Correct answer: 150°

468. Lynne has $8.00 to spend on apples and oranges. Apples cost $0.65 each, and oranges cost $0.75 each. If there is no tax on this purchase and she buys 5 apples, what is the maximum number of whole oranges she can buy?

  • A. 5
  • B. 6
  • C. 7
  • D. 8

Explanation: The correct answer is 6. It's given that apples cost $0.65 each and oranges cost $0.75 each.

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Correct answer: 6

469. The peregrine falcon can reach speeds of up to 200 miles per hour while diving to catch prey, making it the fastest animal on the planet when in a dive.What is a peregrine falcon's maximum speed while diving to catch prey, in feet per second? (Round your answer to the nearest whole number. 1 mile = 5280 feet)

  • A. 289
  • B. 290
  • C. 293
  • D. 295

Explanation: The correct answer is 293. It's given that a peregrine falcon's maximum speed while diving is 200 miles per hour and that 1 mile = 5280…

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Correct answer: 293

470. The peregrine falcon can reach speeds of up to 200 miles per hour while diving to catch prey, making it the fastest animal on the planet when in a dive.If a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (Round your answer to the nearest second.)

  • A. 6
  • B. 7
  • C. 8
  • D. 9

Explanation: The correct answer is 9. If x is the number of hours it will take the falcon to dive 0.5 miles, then the speed of 200 miles per hour can…

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Correct answer: 9

471. In the figure shown, line c intersects parallel lines s and t. What is the value of x ?

  • A. 4 + 5
  • B. 80
  • C. 90
  • D. 75

Explanation: The correct answer is 70. Based on the figure, the angle with measure 110o and the angle vertical to the angle with measure xo are same…

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Correct answer: 4 + 5

472. An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget?

  • A. 0.07
  • B. 15
  • C. 13
  • D. 27

Explanation: Choice C is correct. Let x be the 2015 population of Greenville. It's given that the population increased by 7% from 2015 to 2016.

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Correct answer: 13

473. For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has adefect?

  • A. 1/2,900
  • B. 1/29
  • C. 29/100
  • D. 29/10

Explanation: Choice C is correct. It's given that 29 out of every 100 beads that the machine produces have a defect.

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Correct answer: 29/100

474. Each side of a square has a length of 45. What is the perimeter of this square?

  • A. 180
  • B. 120
  • C. 170

Explanation: The correct answer is 180. The perimeter of a polygon is equal to the sum of the lengths of the sides of the polygon.

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Correct answer: 180

475. The table gives the distribution of votes for a new school mascot and grade level for 80 students. If one of these students is selected at random, what is the probability of selecting a student whose vote for new mascot was for a lion?

  • A. 1/9
  • B. 1/5
  • C. 1/4
  • D. 2/3

Explanation: Choice C is correct. If one of these students is selected at random, the probability of selecting a student whose vote for the new mascot…

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Correct answer: 1/4

476. An object is kicked from a platform. The equation h represents this situation, where h is the height of the object above the ground, in meters, t seconds after it is kicked. Which numberrepresents the height, in meters, from which the object was kicked?

  • A. 0
  • B. 4.9
  • C. 7
  • D. 9

Explanation: Choice D is correct. It's given that the equation h=_4.9 t represents this situation, where h is the height, in meters, of the object t…

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Correct answer: 9

477. 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 = 220 w

Explanation: Choice A is correct. It's given that w represents the total wall area, in square feet.

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Correct answer: P = w/110

478. Which expression is equivalent to (m4 q4 z-1 )(mq5z3) ,where m, q, and z are positive?

  • A. m4 q20 z−3
  • B. m5q9z2
  • C. m6q8z-1
  • D. m20q12z-2

Explanation: Choice B is correct. Applying the commutative property of multiplication, the expression (m4q4z-1) (mq5 z3) can be rewritten as (m4m)(q4…

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Correct answer: m5q9z2

479. 5x + 10x + 16 = 0How many distinct real solutions does the given equation have?

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

Explanation: Choice D is correct. The number of solutions of a quadratic equation of the for max 2 +bx + =c 0, where a, b, and c are constants, can be…

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Correct answer: Zero

480. 3 more than 8 times a number x is equal to 83. Which equation represents this situation?

  • A. (3)(8)x = 8
  • B. 8x = 83 + 3
  • C. 3x + 8 = 83
  • D. 8x + 3 = 83

Explanation: Choice D is correct. The given phrase "8 times a number x" can be represented by the expression 8x.

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Correct answer: 8x + 3 = 83
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