Problem Solving questions are mixed in with Data Sufficiency questions to make up the 37 questions of the GMAT Quantitative section, which must be completed in 75 minutes. The Problems You’ll Work On When working through the problem solving questions test your understanding of: Basic math, including fractions, decimals, ratios and proportions, percents, and exponents. Probability and Statistics, including counting techniques, permutations and combinations, basic probability, arithmetic mean, median, mode, and standard deviation. Algebra, including polynomials, linear equations and... Show more

Problem Solving questions are mixed in with Data Sufficiency questions to make up the 37 questions of the GMAT Quantitative section, which must be completed in 75 minutes.

The Problems You’ll Work On When working through the problem solving questions test your understanding of:

Basic math, including fractions, decimals, ratios and proportions, percents, and exponents.

Probability and Statistics, including counting techniques, permutations and combinations, basic probability, arithmetic mean, median, mode, and standard deviation.

Algebra, including polynomials, linear equations and inequalities, quadratic equations, basic function concepts, and systems of linear equations.

Geometry, including angles, lines, two-dimensional shapes, three-dimensional solids, perimeter, area, surface area, volume, the Pythagorean theorem, and coordinate geometry.

Word problems, including, percentages, rate-time-distance, consecutive integers, ages, work rate, coins, divisibility, factors, multiples, sequences, and equation setup.

Show less

GMAT Quantitative: Problem Solving Practice Test 2

Time left 00:00

25 Questions

1. The enrollment at a middle school increased by 15 percent from the previous year. If the school’s present enrollment is 920 students, how many students were enrolled the previous year?

820890800782846

2. If two identical machines can complete a job in 40 hours, how long, in hours, will it take five such machines to complete the same job?

41682010

3. A field that measures 18 by 30 feet is divided into equal-sized square plots with no land left over. What is the greatest area, in square feet, for each of the square plots?

25936416

4. If a is a positive integer, then (1a)-3(1a2)-2(1a4)-1--> is equivalent to which of the following?

(1a3)-6(1a)-11-->(1a3)-11(1a)-48-->(1a)-6-->

5. Merida and Jude join two different gyms. Merida joins a gym that has a one-time enrollment fee of $70 and $18 per month of membership, including the first month. Jude joins a gym that has a one-time enrollment fee of $40 and $20 per month of membership, including the first month. After how many months of membership will Merida and Jude have paid the same total amount to their respective gyms?

3525152030

6. A realtor selling houses located in a gated community determines that the probability that a model home will be sold is 0.5, the probability that the house next door to the model home will be sold is 0.4, and the probability that at least one of the two houses will be sold is 0.8. What is the probability that the house next door will be sold if the model home is sold first?

0.30.250.20.150.4

7. The units digit of a 3-digit number is 13--> times the hundreds digit and twice the tens digit. What is the number?

126621312216612

8. Consider ab=c-->, where a>0, b>0-->, and c is a positive constant. If b increases by 50%, then what percent change in a should occur, so that the equation remains true?

6623%--> increase3313%--> decrease25% decrease25% increase50% increase

9. If x-2=14-->, then x-4=-->

116-->4-16-->-116-->16

10. Given positive integers w, x, y, and z. If the remainder when w is divided by x is 9 and the remainder when z is divided by y is 7, what is the least value of x+y-->?

1514171618

11. Working alone at its constant rate, Machine A can produce 1,050 electrical components in 5 hours. Machine B, working alone, can produce 1,050 electrical components in 712--> hours. If the two machine work simultaneously for T hours and produce 1,050 electrical components, how many electrical components has Machine B produced at the end of T hours?

210630420525140

12. In the triangle shown angles 1 and 2 are congruent. Determine x.

810769

13. A prime number n is a factor of both (14k+13)--> and (7k+1)-->, where k is a positive integer. What is the value of n?

1311327

14. A recipe for a mulled cranberry punch calls for 234--> cups of cranberry juice, 112--> cups of white grape juice, 213--> cup of water, and 14--> cup of cinnamon sugar. What is the ratio of the total amount, in cups, of fruit juice to the total amount, in cups, of water and cinnamon sugar in the recipe?

31 to 1751 to 3112 to 3131 to 5131 to 12

15. In driving a round trip from City A to City B, a motorist drives to City B and, on the way back to City A, by the same route, stops at a service station at a location that is 10 percent of the distance to City A from City B. When the motorist stops at the service station, what percent of the round trip is completed?

65%45%55%60%40%

16. The formula for lift, the force that holds an airplane in the air, is L=CL(dAV22)-->. When d is measured in pounds per cubic feet, A is measured in square feet, V is measured in feet per second, and if CL--> is a numerical coefficient with no units attached, what are the units for the lift of an airplane?

lbsec2-->lb⋅ftsec2-->lb⋅ftsec-->lb2⋅ft2lb⋅ft2sec2

17. A bag contains 48 tokens, all identical except for color. There are twice as many red as green tokens and twice as many white tokens as black tokens. There are 6 more black tokens than green tokens. If one token is randomly drawn from the bag, what is the probability that the token is red or black?

916-->716-->13-->1116-->516-->

18. Katie, Ace, and Rory interviewed for jobs at companies A, B, and C, respectively. The probability that Katie will get a job offer from company A is 14-->; the probability that Ace will get a job offer from company B is 12-->; and the probability that Rory will get a job offer from company C is 58-->. The three companies have no connections to one another, so the job offers are mutually independent. What is the probability that Katie and Ace will get job offers, but not Rory?

38-->18-->98-->564-->364-->

19. Three of 12 remote controls in a box are defective. The remote controls are tested one at a time and not replaced in the box after testing. What is the probability that neither of the first two remote controls tested is defective?

16-->916-->34-->29-->611-->

20. An appliance store owner ordered 50 countertop microwave ovens to be sold for $144 each, which represents a 20 percent markup over the store owner’s initial cost for each microwave. Of the microwave ovens ordered, 5 were never sold. These ovens were returned for a refund of 50 percent of the owner’s initial cost. What was the owner’s profit or loss as a percent of the initial cost of the 50 microwave ovens?

15% loss13% loss15% profit13% profit10% profit

21. The line segment between points A and B has endpoints 614--> and 612-->. The line segment between points C and D has endpoints 524--> and 322-->. What is the ratio of AB to CD?

12-->2-->-2-->-12-->1

22. The table shows the results of a poll of 320 library patrons who were asked what genre of books they read most often. What is the ratio of the number of patrons who chose nonfiction genres to the number who chose fiction genres?

Genre	Number of Patrons
Biography/Historical Nonfiction	44
Historical Fiction	58
Mystery Fiction	64
Science/Nature Nonfiction	50
Science Fiction/Fantasy	104
Total	320

47113-->11347-->113160-->47160-->47320-->

23. A school district’s food and nutrition director asks a panel of high school students for recommendations for changes in the menu options in the school cafeteria. After implementing student recommendations that were in compliance with state nutrition guidelines, the director surveys 100 randomly selected students in the high school to assess their satisfaction with the revised cafeteria menu, on a scale of 1 (indicating “Extremely Dissatisfied”) to 7 (indicating “Extremely Satisfied). The graph shown displays the students’ responses to the survey. What is the ratio of the number of students who chose 5 or higher as a response to the number of students who chose 3 or lower as a response?

911-->34-->32-->94-->101-->

24. A sequence of consecutive integers begins with 60 and ends with 100. If one integer is randomly selected from the sequence, what is the probability that the integer is even?

2041-->2141-->2140-->1940-->12-->

25. Bag 1 contains 10 blue, 8 gold, and 6 red chips, all identical except for color. Bag 2 contains 8 blue, 2 gold, and 2 red chips, also all identical except for color. Two chips, one from each bag, are randomly drawn, one after the other. What is the probability that neither chip will be gold?

23-->59-->12-->518-->49-->