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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 4 of 32

61. A company that makes wildlife videos purchases camera equipment for $32,400. The equipment depreciates in value at a constant rate for 12 years, after which it is considered to have no monetary value. How much is the camera equipment worth 4 years after it is purchased?

  • A. $10,800
  • B. $16,200
  • C. $21,600
  • D. $29,700

Explanation: Choice C is correct. The value of the camera equipment depreciates from its original purchase value at a constant rate for 12 years.

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Correct answer: $21,600

62. Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

  • A. 38
  • B. 33
  • C. 22
  • D. 16

Explanation: 90% of his earnings each week, so this week he will save 0.9(10x + 80) dollars.

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Correct answer: 22

63. The table shows the kinds of foods that are fed to the cats and dogs currently boarded at a pet care facility. What fraction of the dogs are fed only dry food?

  • A. 2/41
  • B. 2/25
  • C. 7/41
  • D. 2/7

Explanation: Choice B is correct. There are 2 dogs that are fed only dry food and a total of 25 dogs.

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Correct answer: 2/25

64. A certain package requires 3 centimeters of tape to be closed securely. What is the maximum number of packages of this type that can be secured with 6 meters of tape?

  • A. 100
  • B. 150
  • C. 200
  • D. 300

Explanation: Choice C is correct. Multiplying each side of 1 meter = 100 cm by 6 gives 6 meters = 600 cm. Each package requires 3 centimeters of tape.

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Correct answer: 200

65. A customer paid $53.00 for a jacket after a 6 percent sales tax was added. What was the price of the jacket before the sales tax was added?

  • A. $47.60
  • B. $50.00
  • C. $52.60
  • D. $52.84

Explanation: Choice B is correct. Let x be the price, in dollars, of the jacket before sales tax.

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Correct answer: $50.00

66. If 50 one-cent coins were stacked on top of each other in a column, the column would be approximately 3 (7/8) inches tall. At this rate, which of the following is closest to the number of one-cent coins it would take to make an 8-inch-tall column?

  • A. 75
  • B. 100
  • C. 200
  • D. 390

Explanation: Choice B is correct. A column of 50 stacked one-cent coins is about 3(7/8) inches tall, which is slightly less than 4 inches tall.

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Correct answer: 100

67. A survey was given to residents of all 50 states asking if they had earned a bachelor's degree or higher. The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor's degree or higher for all 50 states was 26.95%. What is the difference between the median percent of residents who earned a bachelor's degree or higher for these 7 states and the median for all 50 states?

  • A. 0.05%
  • B. 0.95%
  • C. 1.22%
  • D. 7.45%

Explanation: Choice B is correct. The median of a set of numbers is the middle value of the set values when ordered from least to greatest.

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Correct answer: 0.95%

68. The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?

  • A. 6,020
  • B. 6,027
  • C. 6,440
  • D. 6,468

Explanation: Choice B is correct. The percent increase from 2012 to 2013 was 5,880 - 5,600 / 5,600 = 0.05 or 5%.

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Correct answer: 6,027

69. In 1854, during the California gold rush, each ounce of gold was worth $20, and the largest known mass of gold found in California was worth $62,400 in that year. What was the weight, in pounds, of this mass of gold?

  • A. 188
  • B. 190
  • C. 195
  • D. 198

Explanation: The correct answer is 195. Since the mass of gold was worth $62,400 and each ounce of gold was worth $20, the mass of the gold was 62,400…

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Correct answer: 195

70. The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?

  • A. 20
  • B. 30
  • C. 35
  • D. 40

Explanation: The correct answer is 30. Let x represent the number of correct answers from the player and y represent the number of incorrect answers…

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Correct answer: 30

71. Point C is the center of the circle above. What fraction of the area of the circle is the area of the shaded region?

  • A. 2/18
  • B. 3/18
  • C. 5/18
  • D. 7/18

Explanation: The correct answer is 5 /18. There are 360° in a circle, and it is shown that the central angle of the shaded region is 100°.

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Correct answer: 5/18

72. If 2a/b = 1/2, what is the value of b/a?

  • A. 1/8
  • B. 1/4
  • C. 2
  • D. 4

Explanation: Choice D is correct. Dividing both sides of equation 2a/b = 1/2 by 2 gives a/b = 1/4. Taking the reciprocal of both sides yields b/a = 4.

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Correct answer: 4

73. In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of the 10,000 cars of the same model will have a manufacturing defect?

  • A. 150
  • B. 200
  • C. 250
  • D. 300

Explanation: Choice A is correct. The fraction of the cars in the random sample that have a manufacturing defect is 3/200 = 0.015.

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Correct answer: 150

74. x + 1 = 2/x + 1In the equation above, which of the following is a possible value of x + 1?

  • A. 1 - √2
  • B. √2
  • C. 2
  • D. 4

Explanation: Choice B is correct. Multiplying both sides of the equation by x + 1 gives (x + 1)2 = 2.

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Correct answer: √2

75. On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

  • A. 24.5
  • B. 25
  • C. 25.4
  • D. 26

Explanation: The correct answer is 25.4. The average speed is the total distance divided by the total time.

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Correct answer: 25.4

76. On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?

  • A. 15/50
  • B. 15/40
  • C. 35/50
  • D. 50/135

Explanation: Choice D is correct. The total number of gas station customers on Tuesday was 135.

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Correct answer: 50/135

77. Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey about potential changes to next year's schedule. Of the students selected for the survey, 1/4 were freshmen, and 1/3 were sophomores. Half of the remaining selected students were juniors. If 336 students were selected for the survey, how many were seniors?

  • A. 240
  • B. 140
  • C. 120
  • D. 70

Explanation: Choice D is correct. It is given that the number of students surveyed was 336.

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Correct answer: 70

78. Biologists found a new species of pale shrimp at the world's deepest undersea vent, the Beebe Vent Field. The vent is 3.1 miles below the sea's surface. Approximately how many kilometers below the sea's surface is the vent?

  • A. 2
  • B. 3
  • C. 4
  • D. 5

Explanation: Choice D is correct. It's given that 1 kilometer is approximately equivalent to 0.6214 miles.

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Correct answer: 5

79. Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that the serving size of the cereal is 3/4 cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults.If p percent of an adult's daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x?

  • A. p = 0.5x
  • B. p = 5x
  • C. p = (0.05)x
  • D. p = (1.05)x

Explanation: Choice B is correct. It's given that each serving of Crunchy Grain cereal provides 5% of an adult's daily allowance of potassium, so x…

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Correct answer: p = 5x

80. Near the end of a US cable news show, the host invited viewers to respond to a poll on the show's website that asked, "Do you support the new federal policy discussed during the show?" At the end of the show, the host reported that 28% responded "Yes," and 70% responded "No." Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?

  • A. The percentages do not add up to 100%, so any possible conclusions from the poll are invalid.
  • B. Those who responded to the poll were not a random sample of the population of the United States.
  • C. There were not 50% "Yes" responses and 50% "No" responses.
  • D. The show did not allow viewers enough time to respond to the poll.

Explanation: Choice B is correct. In order for the poll results from a sample of a population to represent the entire population, the sample must be…

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Correct answer: Those who responded to the poll were not a random sample of the population of the United States.
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