Free Quantitative Reasoning MCQs with Answers

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°. Therefore, the area of the shaded region can be represented as a fraction of the area of the entire circle, 100 / 360, which can be reduced to 5 /18 . Either 5/18, .277, or .288 can be gridded as the correct answer.

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.

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. At this rate, out of 10,000 cars, there would be 0.015 × 10,000 = 150 cars that have a manufacturing defect.

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. This means x + 1 is a number whose square is 2, so (x + 1) is either √2 or −√2 . Therefore, √2 is a possible value for x + 1.

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. The total distance is 11 miles and the total time is 26 minutes. Thus, the average speed is 11/26 miles per minute. The question asks for the average speed in miles per hour, and there are 60 minutes in an hour; converting miles per minute to miles per hour gives the following:Average speed = 11 miles/26 minutes × 60 minutes/1 hour= 660/26 miles per hour ≈ 25.38 miles per hourTherefore, to the nearest tenth of a mile per hour, the average speed of Paul Revere's ride would have been 25.4 miles per hour.

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. The table shows that the number of customers who did not purchase gasoline was 50. Finding the ratio of the number of customers who did not purchase gasoline to the total number of customers gives the probability that a customer selected at random on that day did not purchase gasoline, which is 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. Finding 1/4 of 336 yields (1/4)(336) = 84, the number of freshmen, and finding 1/3 of 336 yields (1/3)(336) = 112, the number of sophomores. Subtracting these numbers from the total number of selected students results in 336 − 84 − 112 = 140, the number of juniors and seniors combined. Finding half of this total yields (1/2)(140) = 70, the number of juniors. Subtracting this number from the number of juniors and seniors combined yields 140 − 70 = 70, the number of seniors.

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. Let x be the number of kilometers equivalent to 3.1 miles. The proportion 1 kilometer / 0.6214 = x kilometer / 3.1 miles can be used to solve for the value of x. Multiplying both sides of this equation by 3.1 yields 3.1/ 0.6214 = x, or x ≈ 4.99. This is approximately 5 kilometers.

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 servings would provide x times 5%. The percentage of an adult's daily allowance of potassium, p, is 5 times the number of servings, x. Therefore, the percentage of an adult's daily allowance of potassium can be expressed as 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 representative of the population. A sample that is randomly selected from a population is more likely than a sample of the type described to represent the population. In this case, the people who responded were people with access to cable television and websites, which aren't accessible to the entire population. Moreover, the people who responded also chose to watch the show and respond to the poll. The people who made these choices aren't representative of the entire population of the United States because they were not a random sample of the population of the United States.