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. A thrift shop sells pre-owned hardcover books for $7 each and pre-owned paperback books for $5 each. A customer makes a purchase of both hardcover books and paperback books. Before taxes, the total purchase price of the books is $56. How many total books did the customer purchase?

1078911

2. 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?

2002,0000.0020.000220,000

3. 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?

1528111923

4. Which of the following expressions in simplified form is a rational number?
I. 4646(46)2
II. (46+46)2
III. 4646

II onlyI and II onlyII and III onlyIII onlyI only

5. 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?

10060908070

6. 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$800$1,600$400$2,000

7. In a survey of 600 students, 75% indicated they like orange juice, 40% indicated they like apple juice, and 30% indicated they like grape juice. If all of the survey participants like at least one of these juices and 35% of them like exactly two of these juices, how many survey participants like only one of these juices?

250390260210360

8. 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?

25%38%15%85%2%

9. How many different arrangements to seat four spectators in four of seven empty stadium seats that are all in the same row are possible?

12282435840

10. 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 ?

81.8180.19¯81.81¯80.1981

11. A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

9624080112160

12. Lupita and Vin both swam in the indoor pool at the same gym today. Lupita swims at that gym every 12 days. Vin swims there every 15 days. If both continue with their regular swimming schedules at the gym, the next time both will swim there on the same day is in how many days?

6030124515

13. The distribution of the scores on a standardized test is bell-shaped and is symmetric about its mean, M, with a standard deviation, S. If 68% of the scores fall between M-S and M+S, what percent of the scores are greater than M+S?

8%16%32%4%34%

14. 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?

2232521426

15. 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+K-12120+K240+K+12239+K2240+K-12

16. In the figure shown, CE¯ has length 40 feet, EA¯ has length 20 feet, and DE¯ is perpendicular to AC¯ and has length 10 feet. What is the area, in feet2, of ΔABC?

9003,6002251,800450

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

30π14π24π20π10π

18. 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-d+b500-c-d500-c+d500-b

19. 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?

1313.25151414.25

20. 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?

3.54.252.755.54.75

21. Sofi has S game cards, which is half as many as her older brother has, and three times as many as her younger sister has. In terms of S, how many game cards do the three siblings have altogether?

313S312S43S213S512S

22. Given p is an integer and (0.00005)(0.0005)(0.005)×10p is an integer, what is the least possible value of p?

12-129-90

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

30%75%25%35%60%

24. 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?

8616112316287

25. The arithmetic average of 20 numbers is A. The arithmetic average of 10 of the number is 16. In terms of A, what is the arithmetic average of the remaining 10 numbers?

A-82A-1616-A20A-1616-2A