Free Quantitative Reasoning MCQs with Answers

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. So if x is the amount, in dollars, by which the value of the equipment depreciates each year, the value of the camera equipment, in dollars, t years after it is purchased would be 32,400 - xt. Since the value of the camera equipment after 12 years is $0, it follows that 32,400 - 12x = 0. To solve for x, rewrite the equation as 32,400 = 12x. Dividing both sides of the equation by 12 gives x = 2,700. It follows that the value of the camera equipment depreciates by $2,700 each year. Therefore, the value of the equipment after 4 years, represented by the expression 32,400 - 2,700(4), is $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. The inequality 0.9(10x + 80) ≥ 270 represents the condition that he will save at least $270 for the week. Factoring 10 out of the expression 10x + 80 gives 10(x + 8). The product of 10 and 0.9 is 9, so the inequality can be rewritten as 9(x + 8) ≥ 270. Dividing both sides of this inequality by 9 yields x + 8 ≥ 30, so x ≥ 22. Therefore, the least number of hours Ken must work the rest of the week to save at least $270 for the week is 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. Therefore, the fraction of dogs fed only dry food is 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. The number of packages that can be secured with 600 cm of tape is 600/3, or 200 packages.

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. The price of the jacket after the 6% sales tax is added was $53. This can be expressed by the equation x + 0.06x = 53, or 1.06x = 53. Dividing each side of this equation by 1.06 gives x = 50. Therefore, the price of the jacket before sales tax was $50.

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. Therefore a column of stacked one-cent coins that is 4 inches tall would contain slightly more than 50 one-cent coins. It can then be reasoned that because 8 inches is twice 4 inches, a column of stacked one-cent coins that is 8 inches tall would contain slightly more than twice as many coins; that is, slightly more than 100 one-cent coins. An alternate approach is to set up a proportion comparing the column height to the number of one-cent coins, or 3(7/8) inches / 50 coins = 8 inches / x coins, where x is the number of coins in an 8-inch-tall column. Multiplying each side of the proportion by 50x gives 3(7/8) x = 400. Solving for x gives x = 400 x 8 / 31, which is approximately 103. Therefore, of the given choices, 100 is closest to the number of one-cent coins it would take to build an 8-inch-tall column.

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. If the percents in the table are ordered from least to greatest, the middle value is 27.9%. The difference between 27.9% and 26.95% is 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%. Since the percent increase from 2012 to 2013 was estimated to be double the percent increase from 2013 to 2014, the percent increase from 2013 to 2014 was expected to be 2.5%. Therefore, the number of subscriptions sold in 2014 is expected to be the number of subscriptions sold in 2013 multiplied by (1 + 0.025), or 5,880(1.025) = 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 / 20 = 3120 ounces. Since 1 pound = 16 ounces, 3120 ounces is equivalent to 3120 / 16 = 195 pounds.

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 from the player. Since the player answered 40 questions in total, the equation x + y = 40 represents this situation. Also, since the score is found by subtracting the number of incorrect answers from twice the number of correct answers and the player received a score of 50, the equation 2x - y = 50 represents this situation. Adding the system of two equations together yields (x + y) + (2x - y) = 40 + 50. This can be rewritten as 3x = 90. Finally, solving for x by dividing both sides of the equation by 3 yields x = 30.