Free Quantitative Reasoning MCQs with Answers

81. When a patient receives a penicillin injection, the kidneys begin removing the penicillin from the body. The table and graph above show the penicillin concentration in a patient's bloodstream at 5-minute intervals for the 20 minutes immediately following a one-time penicillin injection.According to the table, how many more micrograms of penicillin are present in 10 milliliters of blood drawn from the patient 5 minutes after the injection than are present in 8 milliliters of blood drawn 10 minutes after the injection?

• A. 570
• B. 576
• C. 578
• D. 580

Explanation: The correct answer is 576. According to the table, 5 minutes after the injection, the penicillin in the patient's bloodstream is 152 micrograms per milliliter. Thus, there are 10 × 152 = 1520 micrograms of penicillin in 10 milliliters of blood drawn 5 minutes after the injection. Similarly, 10 minutes after the injection, the penicillin concentration is 118 micrograms per milliliter. Thus, there are 8 × 118 = 944 micrograms of penicillin in 8 milliliters of blood drawn 10 minutes after the injection. Therefore, there are 1520 − 944 = 576 more micrograms of penicillin in 10 milliliters of blood drawn 5 minutes after the injection than in 8 milliliters of blood drawn 10 minutes after the injection.

82. Human blood can be classified into four common blood types-A, B, AB, and O. It is also characterized by the presence (+) or absence (-) of the rhesus factor. The table shows the distribution of blood type and rhesus factor for a group of people. If one of these people who is rhesus negative (-) is chosen at random, the probability that the person has blood type B is 1/9. What is the value of x?

• A. 5
• B. 6
• C. 7
• D. 8

Explanation: The correct answer is 8. In this group,1/9th of the people who are rhesus-negative have blood type B. The total number of people who are rhesus negative in the group is 7 + 2 + 1 + x, and 2 people are rhesus negative with blood type B. Therefore, 2 /(7 + 2 + 1 + x) = 1/9. Combining like terms on the left-hand side of the equation yields 2/(10+x) = 1/9. Multiplying both sides of this equation by 9 yields 18/(10+x) = 1, and multiplying both sides of this equation by (10 + x) yields 18 = 10 + x. Subtracting 10 from both sides of this equation yields 8 = x.

83. Of the companies surveyed about the skills they required in prospective employees, 20 percent required both computer skills and writing skills. What percent of the companies surveyed required neither computer skills nor writing skills? (1) Of those companies surveyed that required computer skills, half required writing skills. (2) 45 percent of the companies surveyed required writing skills but not computer skills.

• A. statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question
• B. statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question
• C. both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
• D. each statement alone is sufficient
• E. statements (1) and (2) together are not sufficient, and additional data is needed to answer the question

Explanation: Option C gives sufficient information from which it can be concluded that the percentage of companies that did not require neither computer skills nor writing skills using a venn diagram Taking (1) and (2) together, to 85 percent (20 +20+45) i.e 20% required computer skills,20% required both skills,45% required only writing skills.Therefore companies that do not require computer skills nor reading skills,would be equal to 100- 85= 15 percent of the surveyed companies required neither computer skills nor writing skills.All the other options provided are not sufficient enough to conclude the percentage of companies that do not require computer skills nor reading skills.

84. A retail company has 50 large stores located in different areas throughout the state. A researcher for the company believes that employee job satisfaction varies greatly from store to store. Which of the following sampling methods is most appropriate to estimate the proportion of all employees of the company who are satisfied with their jobs?

• A. Selecting one of the 50 stores at random and then surveying each employee at that store
• B. Selecting 10 employees from each store at random and then surveying each employee selected
• C. Surveying the 25 highest-paid employees and the 25 lowest-paid employees
• D. Creating a website on which employees can express their opinions and then using the first 50 responses

Explanation: Choice B is correct. Selecting employees from each store at random is most appropriate because it's most likely to ensure that the group surveyed will accurately represent each store location and all employees.

85. The line parallel to the x-axis is given by:

• A. y = 0
• B. x = 0
• C. y = c
• D. x = c

Explanation: A line parallel to the x-axis is a horizontal line where the y-coordinate remains constant. This is represented by the equation y = c, where c is a constant value.Option A is incorrect because y=0 does not generalize the concept of a line parallel to the x-axis.Option B is incorrect because x=0 represents a vertical line parallel to the y-axis, not the x-axis.Option D is incorrect because x=c represents a vertical line, not a horizontal line parallel to the x-axis.

86. The area of a rectangle is 420 inches and diagonal is 29 inches. Find its sides?

• A. 30, 31
• B. 40, 41
• C. 20, 21
• D. 10, 11

Explanation: To solve for the sides of the rectangle, we use the relationship between the sides, area, and diagonal. By calculating the square of the sides and applying the formula for the area of a rectangle, we can determine the correct sides. In this case, the correct sides are 20 and 21, as they satisfy the given area of 420 inches. The other options do not align with the given area, making them incorrect choices.

87. Six consecutive integers are given. The sum of the first three is 27.What is the sum of the last three?

• A. 29
• B. 30
• C. 32
• D. 36

Explanation: Using the number sequence formula a number sequence can be written down for the six consecutive integers; N being the first integer N,N+1,N+2,N+3,N+4,N+5 If the sum of the first three integers = 27 I.e N+N+1+N+2 = 27 3N+3 = 27 3N = 27-3 = 24 N = 24/3 = 8 N = 8 For the sum of last three integers, the formula is; N+3+N+4+N+5 N = 8 i.e. 8 + 3 + 8 + 4 + 8 + 5 = 36

88. Given that 3≤x≤5 and -4≤y≤-1, the greatest possible value of x/y is:

• A. -1/4
• B. -2/5
• C. -3/4
• D. -3/5

Explanation: To find the greatest possible value of the fraction x/y, where x and y are bounded by the given inequalities, we should consider the smallest value for x and the largest value for y. This is because the fraction x/y will be negative, and a negative fraction is greatest when it is closest to zero.Given the constraints, the smallest value of x is 3 and the largest value of y is -4, resulting in the fraction 3/-4 = -0.75, which is -3/4.Other options such as -1/4, -2/5, and -3/5 are not the greatest possible values because their absolute values are larger (i.e., further from zero) than -3/4.

89. A boy puts a fixed amount of money in a box every week after his birthday. Find 'p'

• A. 34
• B. 37
• C. 40
• D. 43

Explanation: The problem describes a scenario where a boy puts a fixed amount of money in a box every week. By examining the differences between the amounts for consecutive weeks, we determine that the weekly increase is 3. Starting from the 5th week amount of 28, the amount after the 8th week is calculated as follows:After 6th week: 28 + 3 = 31After 7th week: 31 + 3 = 34After 8th week: 34 + 3 = 37Therefore, the correct answer is 37. The other options represent amounts after different numbers of weeks, hence they are incorrect.

90. The area of a circle is 49 π. Find its circumference in term of π.

• A. 14 π
• B. 49/2 π
• C. 49 π
• D. 98 π

Explanation: To find the circumference, first calculate the radius from the area given. The radius is 7, so the circumference is 2π(7) = 14π. The correct answer is Option A. Option B wrongly divides the area, Option C confuses area with circumference, and Option D incorrectly doubles the circumference value.