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.

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GMAT Quantitative: Problem Solving Practice Test 3

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25 Questions

1. Five people are to be seated in five identical chairs that are placed in a circular pattern. How many different seating arrangements of the five people (relative to each other) are possible?

10252412060

2. The integer K=3a2+6b2-->, where a and b are positive integers such that their greatest common factor is 2. What is the greatest even number that must be a factor of K?

1243624

3. If A is a positive integer such that y=6A5x2, x≠0-->, then x=-->

±6A5y-->±6Ay5-->6A5y-->±6A5y-->6A5y-->

4. If K is a positive integer such that the remainder when 17 is divided by K is 2, what is the sum of all the possible values of K?

823201825

5. Two consecutive angles of a parallelogram have angle measures, in degrees, of 2x-30--> and x+60-->. What is the measure, in degrees, of the smaller angle?

601007050110

6. A solution of salt and water is 10 percent salt by weight. After a period of time under pressure and heat, a portion of the water evaporates so that the solution is 40 percent salt by weight. What is the ratio of the initial weight of water to the final weight of water in the solution?

1 to 41 to 31 to 66 to 14 to 1

7. The price of season tickets this year is 25% more than the price last year. Last year’s price is what percent of this year’s price?

75%120%90%125%80%

8. If 3 is one root of the quadratic equation 2x2-5x+k=2-->, where k is a constant, what is the equation’s other root?

12-->-3-->-1-->-12-->3

9. If x is an integer such that |2x+1|<3-->, then which of the following is a possible value of x3+2x2+5x+10-->?
I. 0
II. 6
III. 10

I, II, IIIII and III onlyI onlyI and II onlyII only

10. The positive integer N is not divisible by 2 or 4. What is the sum of the possible remainders when N is divided by 8?

911151316

11. The scoring formula for a timed, 50-question test is S=C-14B-->, where S is the score on the test, C is the number of questions answered correctly and B is the number of questions that were left unanswered. A student answers 42 questions and leaves 8 questions unanswered. Which of the following could be the student’s score?
I. -2-->
II. 40
III. 41

I and III onlyIII onlyI and II onlyII onlyI only

12. Jayma has applied to graduate programs at both university A and university B. The probability that Jayma will receive an acceptance letter from university A is 0.45; the probability she will receive an acceptance letter from university B is 0.36; and the probability she will receive an acceptance letter from both universities is 0.17. What is the probability that Jayma will receive an acceptance letter from at least one of the two universities?

0.640.810.980.410.26

13. Mani saves money in a jar at home for six months. The first month he saves S dollars. Each month thereafter, Mani saves 12--> of what he has saved the previous month. If Mani’s total savings at the end of the six months is $393.75, how much money does he save the sixth month?

$12.50$6.25$25.00$18.75$7.50

14. In triangle PQR shown, PQ=PR--> and x=50-->. What is the value of y?

6545809050

15. As shown in the following figure, a space diagonal in a rectangular prism is a line that goes from a vertex of the prism, through the center of the prism to the opposite vertex. What is the length of the space diagonal of a 3 by 4 by 12 rectangular prism?

515131125

16. When positive integer N is divided by 7, the remainder is x, and when positive integer M is divided by 11, the remainder is y. What is the greatest value for x+y-->?

1815141716

17. If a≥0-->, then (a34)18=-->

a94-->a23-->a43-->a34-->a392-->

18. The original price of a jacket is reduced by 15 percent for a one-day sale at an online store. After the sale ends, the sale price of the jacket is increased by 20 percent. The final price of the jacket is what percent of its original price?

102%105%95%98%120%

19. Rose read a novel that has 208 pages in four days. Each day she read 20 more pages than she read the previous day. How many pages did Rose read on the first day?

2028242622

20. How many different meal combinations consisting of one entrée, one vegetable side dish, one nonalcoholic beverage, and one dessert are possible from a selection of 10 entrées, 12 vegetable side dishes, 5 nonalcoholic beverages, and 6 desserts?

3,60033720300600

21. In a survey of students at a certain college, participants were asked two questions. If 23--> of those surveyed responded “Strongly Agree” to the first question, and of those respondents, 15--> answered “Strongly Agree” to the second question, what portion of the survey participants did not answer “Strongly Agree” to both questions?

1315-->35-->56-->34-->215-->

22. If (4x)(8y)=128-->, what is the value of x when y=3-->?

-2-->-1-->12-->0-32-->

23. Babia has seven more marbles than three times the number of marbles that Joe has. If Babia has B marbles and Joe has J marbles, which of the following is a possible value for B?
I. 10
II. 18
III. 49

I, II, and IIII and III onlyI onlyIII onlyII only

24. If x≠0-->, then (x-7x-11)-12=-->

1x2-->x4-->x9-->1x-->x2-->

25. If Z=N(11+N-1)-1-->, then 10ZN+1=-->

10(N+1)2-->10N-->51010N+1-->