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 1

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25 Questions

1. The attendance on the first day of a 3-day festival was 20% greater than the attendance on the final day of the festival. If the attendance on the first day was 11,418, what was the attendance on the final day of the festival?

3,8069,13411,1945,1909,515

2. Sixty percent of the members of a university orchestra are seniors and 45 percent of those seniors are in the university band. If one member of the university orchestra is randomly selected, what is the probability that the member is a senior band member?

0.450.300.150.750.27

3. A family’s monthly budget allocates $3,600 for their home mortgage payment plus food and utilities in the ratio of 5:3:1, respectively. What is the dollar amount allocated for food?

$1,200$2,000$400$800$1,600

4. A certain car model averages 25 miles per gallon of gasoline. A certain truck model averages 12 miles per gallon of gasoline. If each vehicle is driven 1,200 miles, how much more gasoline (in gallons) will the truck use than the car?

4868522632

5. The ratio of the length of a rectangular patio to its width is 3.5 to 2. If the rectangle’s width is 18 feet, its length, in feet, is closest to which of the following?

2232261452

6. Ninety percent of a large field is cleared for planting. Of the cleared land, 50% is planted with blueberry plants and 40% is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?

4,0008,0003,6002,9163,240

7. Which of the following is the value of 0.00000625?

0.050.50.0050.00250.025

8. The mean of a list of six different positive integers is 68. Four of the integers in the list are 38, 57, 65, and 86. What is the maximum possible value of the greatest of the six integers?

1231628716186

9. A furniture store reduces the retail price of a sofa from $800 to $600. By what percent is the price of the sofa reduced?

25%35%60%75%30%

10. Two vehicles leave the same location at the same time. The first vehicle travels due east at 70 miles per hour. The other vehicle travels due west at 60 miles per hour. Assuming they continue at their respective speeds without stopping, how long (in hours) will it take for the two vehicles to be 455 miles apart?

4.753.55.54.252.75

11. A rectangular flower garden is twice as long as it is wide. If its perimeter is 180 feet, what is the garden’s length, in feet?

80709060100

12. The figure shows a triangle inscribed in a semicircle. If PQ=16 and QR=12, what is the length of arc PQR?

10π30π14π20π24π

13. Last year, the ratio of nonfiction to fiction books in a home library was 1 to 30. This year, the number of nonfiction books increased by 5 and the number of fiction books increased by 50, making the ratio of nonfiction to fiction books 1 to 25. What was the number of nonfiction books last year?

51510128

14. If X=0.81¯, where the bar over the 2-digit sequence 81 indicates the sequence repeats indefinitely, what is the value of 99 X ?

81.81¯80.1980.19¯81.8181

15. One inlet pipe can fill an empty cistern to 13 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 34 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

3.754.753.64.253.25

16. In a list of K consecutive integers, the median is 240. If K is an odd number, what is the greatest integer in the list?

239+K2239+K-12240+K+12120+K240+K-12

17. The range of the six numbers 20, 6, 14, 8, 28, and K is 24. The greatest possible value of K is how much greater than the least possible value of K?

244302634

18. In the xy-plane, which of the following points must lie on the line mx+4y=8 for every possible value of m?
I. (2,0)
II. (2,2)
III. (0,2)

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

19. A mother, who is 37 years old, and her son, who is 9 years old, have the same birthday anniversary month and day. In how many years from now will the mother be twice as old as her son?

1523281911

20. A restaurant chef always mixes 6 ounces of red quinoa with every 16 ounces of white quinoa. How many ounces of red quinoa does the chef put in a 110-ounce mixture of the two grain-like seeds?

1610308060

21. What is the value of (4+6-4-6)2?

128-210026610

22. The enrollment at a local private school for the new school year is 10% more than the enrollment at this time last year. The number of female students increased by 5%, and the number of male students increased by 20%. Female students make up what fraction of the current enrollment at the private school?

451215411711

23. In a high school election in which only seniors and juniors could vote, one candidate, a high school senior, received 400 of the votes cast by the seniors and 10% of the total votes cast by the juniors. If V is the total number of votes cast in the election and 40% of the total votes were cast by seniors, which of the following expressions represents the number of votes that the candidate received?

400+0.70V720+0.10V320+0.06V400+0.40V400+0.06V

24. If n is an integer such that 15<n<250, for how many possible values of n is n5 the square of a prime number?

FourThreeTwoSixFive

25. The partially completed probability tree diagram shows the chances of an outdoor concert taking place or being canceled when rain might or might not occur. What is the probability that the concert takes place given that it rains?

85%2%38%15%25%