Free Quantitative Reasoning MCQs with Answers

481. To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49, with an associated margin of error of 0.04. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?

• A. It is plausible that the proportion is between 0.45 and 0.53.
• B. It is plausible that the proportion is less than 0.45.
• C. The proportion is exactly 0.49.
• D. It is plausible that the proportion is greater than 0.53.

Explanation: Choice A is correct. It's given that the estimate for the proportion of the population that has the characteristic is 0.49 with an associated margin of error of 0.04. Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true proportion of the population that has the characteristic. Therefore, it's plausible that the proportion of the population that has this characteristic is between 0.45 and 0.53.

482. The table summarizes the distribution of color and shape for 100 tiles of equal area.If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.)

• A. 3/10
• B. 5/10
• C. 7/10
• D. 9/10

Explanation: The correct answer is 3/10. It's given that there are a total of 100 tiles of equal area, which is the total number of possible outcomes. According to the table, there are a total of 30 red tiles. The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. By definition, the probability of selecting a red tile is given by 30/100, or 3/10. Note that 3/10 and .3 are examples of ways to enter a correct answer.

483. What length, in centimeters, is equivalent to a length of 51 meters? (1 meter = 100 centimeters)

• A. 0.051
• B. 0.51
• C. 5,100
• D. 51000

Explanation: Choice C is correct. Since 1 meter is equal to 100 centimeters, 51 meters is equal to 51 meters (100 centimeters / 1 meter), or 5,100 centimeters.

484. 6x + 7y = 28 2x + 2y = 10The solution to the given system of equations is (x, y). What is the value of y ?

• A. -2
• B. 7
• C. 14
• D. 18

Explanation: First, let's rearrange the second equation to solve for y. Multiply both sides by 2 to get:4x + 4y = 20Now we can eliminate x by subtracting the second equation from the first equation:(6x + 7y) - (4x + 4y) = 28 - 202x + 3y = 8Subtracting corresponding terms gives:2x - 4x + 3y - 4y = 8 - 20- 2x - y = - 12Now solve for y:- y = - 12 + 2xy = 12 - 2xWe can substitute this value of y into the second equation:2x + 2(12 - 2x) = 102x + 24 - 4x = 10- 2x + 24 = 10- 2x = - 14x = 7Now substitute the value of x into the equation we found for y:y = 12 - 2(7)y = 12 - 14 y = -2So the solution to the system of equations is (x, y) = (7, -2). Therefore, the value of y is -2.

485. Data set A consists of the heights of 75 buildings and has a mean of 32 meters. Data set B consists of the heights of 50 buildings and has a mean of 62 meters. Data set C consists of the heights of the 125 buildings from data sets A and B. What is the mean, in meters, of data set C?

• A. 44
• B. 54
• C. 64
• D. 34

Explanation: The correct answer is 44. The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It's given that data set A consists of the heights of 75 buildings and has a mean of 32 meters. This can be represented by the equation x / 75 =32, where x represents the sum of the heights of the buildings, in meters, in data set A. Multiplying both sides of this equation by 75 yields x =75 (32), or x =2,400 meters. Therefore, the sum of the heights of the buildings in data set A is 2,400 meters. It's also given that data set B consists of the heights of 50 buildings and has a mean of 62 meters. This can be represented by the equation 50y = 62, where y represents the sum of the heights of the buildings, in meters, in data set B. Multiplying both sides of this equation by 50 yields y = 50(62), or y =3,100 meters. Therefore, the sum of the heights of the buildings in data set B is 3,100 meters. Since it's given that data set C consists of the heights of the 125 buildings from data sets A and B, it follows that the mean of data set C is the sum of the heights of the buildings, in meters, in data sets A and B divided by the number of buildings represented in data sets A and B, or 2400+3100/125 which is equivalent to 44 meters. Therefore, the mean, in meters, of data set C is 44.

486. The dot plots represent the distributions of values in data sets A and B.Which of the following statements must be true? I. The median of data set A is equal to the median of data set B. II. The standard deviation of data set A is equal to the standard deviation of data set B.

• A. I only
• B. II only
• C. I and II
• D. Neither I nor II

Explanation: Choice A is correct. The median of a data set with an odd number of values that are in ascending or descending order is the middle value of the data set. Since the distribution of the values of both data set A and data set B form symmetric dot plots, and each data set has an odd number of values, it follows that the median is given by the middle value in each of the dot plots. Thus, the median of data set A is 13, and the median of data set B is 13. Therefore, statement I is true. Data set A and data set B have the same frequency for each of the values 11, 12, 14, and 15. Data set A has a frequency of 1 for values 10 and 16, whereas data set B has a frequency of 2 for values 10 and 16. Standarddeviation is a measure of the spread of a data set; it is larger when there are more values further from the mean, and smaller when there are more values closer to the mean. Since both distributions are symmetric with an odd number of values, the mean of each data set is equal to its median. Thus, each data set has a mean of 13. Since more of the values in data set A are closer to 13 than data set B, it follows that data set A has a smaller standard deviation than data set B. Thus, statement II is false. Therefore, only statement I must be true.

487. Mr. Ali gave a quiz. The results for two of his classes are shown on the box and whisker plots below.Which statement best describe the quiz results?

• A. Class A performed better than Class B.
• B. The lower extreme of Class B is greater than the lower extreme of Class A
• C. Class B has a smaller range of scores in the upper quartile than Class A.
• D. The medians for the two classes are the same.

Explanation: Answer: D. The medians for the two classes are the same.. Explanation: Step 1: Calculate the median for each class. Step 2: Compare the medians of Class A and Class B.Step 3: Calculate the range of scores in the upper quartile for each class.Step 4: Compare the range of scores in the upper quartile for Class A and Class B..

488. A nurse has to record her temperature in Celsius but her thermometer reads Fahrenheit. A patient's temperature is 100.7°F. What is the temperature in °C?(C x 9/5) +32= F

• A. 32 °C
• B. 36.5°C
• C. 38.2 °CStart by taking the number in Fahrenheit and subtracting 32. Then divide the number by 9, and then multiply it by 5. This is how you convert Fahrenheit to Celsius or use the equation C = (F - 32) Ã- 5/9In this case, the answer is about 38.167 degrees Celsius.
• D. 213.3°C

Explanation: Start by taking the number in Fahrenheit and subtracting 32. Then divide the number by 9, and then multiply it by 5. This is how you convert Fahrenheit to Celsius or use the equation C = (F - 32) Ã- 5/9In this case, the answer is about 38.167 degrees Celsius.

489. The dimensions of an examination room are 32 feet by 27 feet. If distance between chairs should be 4 feet in all directions and the size of each chair is 2 X 2 square feet, then the maximum number of chairs placed in the room is(Note: The distance from each wall is not necessarily 4 feet)

• A. 124
• B. 160
• C. 150
• D. 157

Explanation: Let's break this down step by step:1. Room dimensions: 32 feet x 27 feet2. Distance between chairs: 4 feet (in all directions)3. Chair size: 2 feet x 2 feet (square)First, let's find the total available floor space:32 feet x 27 feet = 864 square feetSince each chair occupies a 2x2 square feet area, the total area occupied by one chair is:2 feet x 2 feet = 4 square feetNow, let's calculate the maximum number of chairs that can fit in the room:864 square feet (available floor space) ÷ 4 square feet (area per chair) = 216 chairsHowever, we need to subtract the areas occupied by the "corridors" between chairs, which are 4 feet wide. Let's calculate the total area of these corridors:- Lengthwise corridors (32 feet long): 32 feet x 4 feet = 128 square feet- Widthwise corridors (27 feet wide): 27 feet x 4 feet = 108 square feetTotal corridor area: 128 + 108 = 236 square feetNow, subtract this area from the total available floor space:864 square feet - 236 square feet = 628 square feetFinally, divide the remaining area by the area per chair:628 square feet ÷ 4 square feet (area per chair) = 157 chairsSo, the maximum number of chairs that can be placed in the room is 157.

490. if px3+qx2-ax+b=2x3-3x2-4x=5 then values of p, q. a and b are respectively.

• A. 2, 3, 5, 4
• B. 2, 3, 5, -4
• C. 2,- 3, 4, 5
• D. -2, 3, 4, -5

Explanation: Putting in 2, -3, 4,5 for values of p, q, a, and b respectively will make the right side of the equation the same as the left side allowing the equation to be correct for any value of x put in.