Quantitative Reasoning MCQs

Question 1

The volume of a sphere is given by the formula V = 4/3πr3, where r is the radius of the sphere. Which of the following gives the radius of the sphere in terms of the volume of the sphere?

Accepted Answer

3√3V/4π

Answer

r = 4π⁄3V

Answer

r = 3V⁄4π

Answer

r = 3√4π⁄3V

Question 2

The maximum value of a data set consisting of 25 positive integers is 84. A new data set consisting of 26 positive integers is created by including 96 in the original data set. Which of the following measures must be 12 greater for the new data set than for the original data set?

Accepted Answer

The range

Answer

The mean

Answer

The median

Answer

The standard deviation

Question 3

The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of people she had invited the previous year. If f n is the number of people invited to the fund-raiser n years after Eleanor began organizing the event, which of the following statements best describes the function f?

Accepted Answer

The function f is an increasing exponential function.

Answer

The function f is a decreasing linear function.

Answer

The function f is an increasing linear function.

Answer

The function f is a decreasing exponential function.

Question 4

Some values of x and their corresponding values of y are shown in the table, where a is a constant. If there is a linear relationship between x and y, which of the following equations represents the relationship?

Accepted Answer

x + 2y = a

Answer

x + 2y = 5a

Answer

2x - y = -5a

Answer

2x - y = 7a

Question 5

700, 1200, 1600, 2000, xIf the mean of the five numbers above is 1600, what is the value of x?

Accepted Answer

2500

Answer

2300

Answer

2400

Answer

2600

Question 6

Tilly earns p dollars for every w hours of work. Which expression represents the amount of money, in dollars, Tilly earns for 39w hours of work?

Accepted Answer

39p

Answer

p/39

Answer

p + 39

Answer

p - 39

Question 7

For the right triangle shown, a = 4 and b = 5. Which expression represents the value of c ?

Accepted Answer

√42 + 52

Answer

4 + 5

Answer

√(4)(5)

Answer

√4 + 5

Question 8

The equation E(t) = 5(1.8)t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?

Accepted Answer

The estimated number of employees when the restaurant opened

Answer

The increase in the estimated number of employees each year

Answer

The number of years the restaurant has been open

Answer

The percent increase in the estimated number of employees each year

Question 9

Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?

Accepted Answer

Increasing exponential

Answer

Decreasing exponential

Answer

Decreasing linear

Answer

Increasing linear

Question 10

The population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k ?

Accepted Answer

1.07

Answer

0.07

Answer

0.7

Answer

1.7

Question 11

An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget?

Accepted Answer

16

Answer

0.07

Answer

15

Answer

27

Question 12

If 4x − 4 = 112, what is the positive value of x − 1 ?

Accepted Answer

28

Answer

18

Answer

38

Answer

40

Question 13

What is the y-intercept of the graph shown?

Accepted Answer

(0, 8)

Answer

(−8, 0)

Answer

(−6, 0)

Answer

(0, 6)

Question 14

The function f is defined by f(x) = x3 + 15. What is the value of f (2) ?

Accepted Answer

23

Answer

20

Answer

21

Answer

24

Question 15

Each side of a square has a length of 45. What is the perimeter of this square?

Accepted Answer

180

Answer

120

Answer

170

Answer

200

Question 16

Sean rents a tent at a cost of $11 per day plus a onetime insurance fee of $10. Which equation represents the total cost c, in dollars, to rent the tent with insurance for d days?

Accepted Answer

c = 11d +10

Answer

c = 11(d + 10)

Answer

c = 10(d + 11)

Answer

c = 10d +11

Question 17

John paid a total of $165 for a microscope by making a down payment of $37 plus p monthly payments of $16 each. Which of the following equations represents this situation?

Accepted Answer

16p + 37 = 165

Answer

16p − 37 = 165

Answer

37p − 16 = 165

Answer

37p + 16 = 165

Question 18

A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg,did the rocket burn each second after launch

Accepted Answer

4,995

Answer

17,243

Answer

39,481

Answer

104,895

Question 19

The graph represents the total charge, in dollars, by an electrician for x hours of work. The electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

Accepted Answer

The electrician's hourly rate

Answer

The total amount that the electrician charges

Answer

The electrician's onetime fee

Answer

The maximum amount that the electrician charges

Question 20

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

Accepted Answer

24

Answer

6

Answer

10

Answer

14

Free Quantitative Reasoning MCQs with Answers