Free Quantitative Reasoning MCQs with Answers

441. Following the principles of community-based participatory research, tribal nations and research institutions are equal partners in health studies conducted on reservations. A collaboration between the Crow Tribe and Montana State University _ this model: tribal citizens worked alongside scientists to design the methodology and continue to assist in data collection.Which choice completes the text with the most logical and precise word or phrase?

• A. circumvents
• B. eclipses
• C. fabricates
• D. exemplifies

Explanation: Choice D is the best answer because it most logically completes the text's discussion of the collaboration between the Crow Tribe and Montana State University. As used in this context, "exemplifies" means demonstrates. The text conveys how the Crow Tribe-Montana State University collaboration serves to illustrate the model of community-based participatory research introduced earlier in the text and expanded on later in the text.

442. Given that the conditions in binary star systems should make planetary formation nearly impossible, it's not surprising that the existence of planets in such systems has lacked _ explanation. Roman Rafikov and Kedron Silsbee shed light on the subject when they used modeling to determine a complex set of factors that could support planets' development. Which choice completes the text with the most logical and precise word or phrase?

• A. a discernible
• B. a straightforward
• C. an inconclusive
• D. an unbiased

Explanation: Choice B is the best answer because it most logically completes the text's description of efforts to explain the existence of planets in binary star systems. As used in this context, describing an explanation as "a straightforward" one would mean that the explanation is direct and uncomplicated. The text asserts that since it should be "nearly impossible" for planets to form in binary star systems, it's "not surprising" that there isn't a straightforward explanation for the existence of planets in such systems; the fact that one potential approach involves "complex" factors offers further contextual support for this idea.

443. Seminole/Muscogee director Sterlin Harjo _ television's tendency to situate Native characters in the distant past: this rejection is evident in his series Reservation Dogs, which revolves around teenagers who dress in contemporary styles and whose dialogue is laced with current slang. Which choice completes the text with the most logical and precise word or phrase?

• A. repudiates
• B. proclaims
• C. foretells
• D. recants

Explanation: Choice A is the best answer because it most logically completes the text's discussion of Sterlin Harjo's approach to representing Native characters on television. As used in this context, "repudiates" means rejects or refuses to have anything to do with. The text indicates that television shows tend to depict Native characters as living long ago, but that Harjo's series Reservation Dogs focuses on Native teenagers in the present day, representing a "rejection" of the typical approach to depicting Native characters. This context thus indicates that Harjo repudiates television's general tendency regarding Native characters

444. Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with 1 gallon of water? (1 gallon = 128 fluid ounces)

• A. 16
• B. 8
• C. 4
• D. 3

Explanation: Choice B is correct. It is given that the volume of the glass is approximately 16 fluid ounces. If Jenny has 1 gallon of water, which is 128 fluid ounces, she could fill the glass 128/16 = 8 times.

445. Roberto is an insurance agent who sells two types of policies: a $50,000 policy and a $100,000 policy. Last month, his goal was to sell at least 57 insurance policies. While he did not meet his goal, the total value of the policies he sold was over $3,000,000. Which of the following systems of inequalities describes x, the possible number of $50,000 policies, and y, the possible number of $100,000 policies, that Roberto sold last month?

• A. x + y < 57 50,000x + 100,000y < 3,000,000
• B. x + y > 57 50,000x + 100,000y > 3,000,000
• C. x + y < 57 50,000x + 100,000y > 3,000,000
• D. x + y > 57 50,000x + 100,000y < 3,000,000

Explanation: Choice C is correct. Since Roberto sells only two types of policies and he didn't meet his goal of selling at least 57 policies, the sum of x, the number of $50,000 policies, and y, the number of $100,000 policies, must be less than 57. Symbolically, that is x + y < 57. The total value, in dollars, from selling x number of $50,000 policies is 50,000x. The total value, in dollars, from selling y number of $100,000 policies is 100,000y. Since the total value of the policies he sold was over $3,000,000, it follows that 50,000x + 100,000y > 3,000,000. Only choice C has both correct inequalities.

446. A granite block in the shape of a right rectangular prism has dimensions 30 centimeters by 40 centimeters by 50 centimeters. The block has a density of 2.8 grams per cubic centimeter. What is the mass of the block, in grams? (Density is mass per unit volume.)

• A. 336
• B. 3,360
• C. 16,800
• D. 168,000

Explanation: Choice D is correct. Since density is mass per unit volume, the mass is the density times volume. The volume of a right rectangular prism is the product of the lengths of the sides. Therefore: mass = (2.8 grams per cubic centimeter) × (30 centimeters × 40 centimeters × 50 centimeters) mass = (2.8 grams per cubic centimeter) × (60,000 cubic centimeters) mass = 168,000 grams

447. The table shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages?

• A. mode < median < mean
• B. mode < mean < median
• C. median < mode < mean
• D. mean < mode < median

Explanation: Choice A is correct. The mode is the data value with the highest frequency. So for the data shown, the mode is 18. The median is the middle data value when the data values are sorted from least to greatest. Since there are 20 ages ordered, the median is the average of the two middle values, the 10th and 11th, which for these data are both 19. Therefore, the median is 19. The mean is the sum of the data values divided by the number of the data values. So for these data, the mean is (18 × 6) + (19 × 5) + (20 × 4) + (21 × 2) + (22 × 1) + (23 × 1) + (30 × 1) / 20 = 20. Since the mode is 18, the median is 19, and the mean is 20, mode < median < meanAlternate approach: After determining the mode, 18, and the median, 19, it remains to determine whether the mean is less than 19 or more than 19. Because the mean is a balancing point, there is as much deviation below the mean as above the mean. It is possible to compare the data to 19 to determine the balance of deviation above and below the mean. There is a total deviation of only 6 below 19 (the 6 values of 18); however, the data value 30 alone deviates by 11 above 19. Thus the mean must be greater than 19.

448. To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?

• A. The mean number of children per household in the community is 2.4.
• B. A determination about the mean number of children per household in the community should not be made because the sample size is too small.
• C. The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.
• D. The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.

Explanation: Choice C is correct. In order to use a sample mean to estimate the mean for a population, the sample must be representative of the population (for example, a simple random sample). In this case, Tabitha surveyed 20 families in a playground. Families in the playground are more likely to have children than other households in the community. Therefore, the sample isn't representative of the population. Hence, the sampling method is flawed and may produce a biased estimate.

449. The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height h, in feet, of the front of the roller-coaster car s seconds after it starts up the hill?

• A. h = 8s + 15
• B. h = 15s + 335/8
• C. h = 8s + 335/15
• D. h = 15s + 8

Explanation: Choice A is correct. It's given that the front of the roller-coaster car starts rising when it's 15 feet above the ground. This initial height of 15 feet can be represented by a constant term, 15, in an equation. Each second, the front of the roller-coaster car rises 8 feet, which can be represented by 8s. Thus, the equation h = 8s + 15 gives the height, in feet, of the front of the roller-coaster car s seconds after it starts up the hill.

450. The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?

• A. Mean
• B. Median
• C. Range
• D. Standard deviation

Explanation: Choice B is correct. The median weight is found by ordering the horses' weights from least to greatest and then determining the middle value from this list of weights. Decreasing the value for the horse with the lowest weight doesn't affect the median since it's still the lowest value.