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. What is the probability that a randomly selected integer from a list of consecutive integers from 101 to 500 will have a hundreds digit of 3?

1534142513

2. 516+(38)(23)4-38=

91334015161916

3. 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?

2,9163,6004,0008,0003,240

4. If a and b are positive numbers such that a+b=2, which of the following could be a value of 50a-100b?
I. 150
II. 100
III. 50

II onlyI and III onlyII and III onlyIII onlyI only

5. What is the difference between the mean and the median of the positive numbers, k, k+3, k+4, k+8, k+9, k+12?

12k065k

6. 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?

85151012

7. A painter was paid $800 as labor cost for painting the exterior of the front of a house. This amount was the painter’s estimated labor cost based on a regular rate of R, in dollars per hour, for an estimated time T, in hours. However, the actual time it took for the painter to do the job was 4 hours longer than the estimated time, thereby reducing the hourly rate for the job by $10 per hour. What is R, the painter’s regular rate, in dollars per hour?

4030502060

8. Solution X contains 4 × 10^–2 grams of sugar. Solution Y contains 8 × 10² grams of sugar. The number of grams of sugar in solution Y is how many times the number of grams of sugar in solution X?

20,0000.00022002,0000.002

9. If 15n=15k+15k+15k+15k+15k, then n expressed in terms of k is

3kk5k-1k+11-k

10. 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?

FiveSixThreeTwoFour

11. What is the greatest integer p, for which 3p is a factor of 21! ?

11810129

12. Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, weighing an average of 15.25 kilograms, are shipped to the same location. What is the average weight, in kilograms, of the 20 boxes shipped to the location?

13.2514.25151413

13. If x3=3, then x =

6271993

14. A black and white drawing shows four circles of equal radius. Three of the circles are each divided into k equal parts, where k>5. The fourth circle is divided into k-4 equal parts. A child colors one of the k parts in each of the three circles, and one of the k-4 parts in the fourth circle. What part of a whole circle did the child color?

4k-8k(k-4)2k-4k(k-4)4k-12k(k-4)4k-4k(k-4)k+4k(k-4)

15. If f(x)=(x-1x+1)2, x≠-1, which of the following expressions is equivalent to f(1a), a≠0?

(1-a1+a)2-a2-1a2+1a2-1a2+1-(a-1a+1)1-a21+a2

16. The data in the table show cell phone ownership status by grade level of 300 middle school students. If one of the 300 students is randomly selected, what is the probability that the student owns a cell phone, given that the student is a seventh grader?

Grade Level	Owns a Cell Phone	Does not own a Cell Phone	Totals
Sixth	30	70	100
Seventh	55	45	100
Eighth	78	22	100
Totals	163	137	300

111005516316330011201160

17. In the xy-plane, find the area of a circle that has center (-4,1) and passes through the point (2,-5)?

12π72π40π20π52π

18. What amount (in milliliters) of a 1% sulfuric acid solution must be added to 60 milliliters of a 6% sulfuric acid solution to yield a 5% sulfuric acid solution?

1520124518

19. If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?

214063015

20. The length (in feet) of a rectangle is 4 more than twice its width. The area of the rectangle is 70 feet2. What is the length (in feet) of the rectangle?

10141257

21. 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?

3252266848

22. In a survey of 500 students regarding pet ownership of cats and dogs, c students own at least one cat, d students own at least one dog, and b students own at least one dog and at least one cat. How many students own neither a cat nor a dog?

500-c-d+b500-c-d500-c+d500-b500-c-d-b

23. If xy≠0, then 5x+3y=

3x+5yxy3x+5yx+y8x+y5x+3yxy8xy

24. Given (562)(9k)=N, which of the following equals (562)(9k+1)?

N+(9k+1)N+1N+562N+563N+9k

25. Set M consists of all positive integers that are multiples of 4. Set N consists of all positive integers less than 100 that have a units digit of 8. How many integers do sets M and N have in common?

SevenThreeFourSixFive