Problem Solving

Problem Solving is the backbone of the GMAT Quant section: a question stem, five answer choices, and a two-minute budget. The questions here span arithmetic, algebra, geometry, number properties, inequalities, and word problems — the same mix you will see on test day. Work them untimed while you rebuild fundamentals, then switch to the timer and practice committing to an answer under the clock. Every question includes a full written explanation, so review the ones you miss and log them in your error log: on Quant, most score improvement comes from eliminating repeat mistakes, not from seeing more new questions.

Official GMAT Problem Solving questions with difficulty ratings and topic tags.·Show:20 30 50

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655-705 (Hard)

A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

505-555 (Easy)

A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

Sub 505 (Easy)

The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

555-605 (Medium)

Jan lives x floors above the ground floor of a highrise building. It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator. If it takes Jan the same amount of time to walk down the steps to the ground floor as to wait for the elevator for 7 minutes and ride down, then x equals

555-605 (Medium)

For how many integers n is 2^n = n^2 ?

655-705 (Hard)

Which of the following statements can be inferred from the data above? I. The Klein family's annual income more than doubled from 1985 to 1995. II. The Klein family's annual income increased by a greater amount from 1985 to 1990 than from 1990 to 1995. III. The Klein family's average (arithmetic mean) annual income for the period shown was greater than $40,000.

Sub 505 (Easy)

Last year if 97 percent of the revenues of a company came from domestic sources and the remaining revenues, totaling $450,000, came from foreign sources, what was the total of the company's revenues?

555-605 (Medium)

A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, average number sold was 84, and among the male members, the average number sold was 96. What was the ratio of the number of male members to the number of female members in the club?

Sub 505 (Easy)

If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1 ?

Sub 505 (Easy)

A certain college has a student-to-teacher ratio of 11 to 1. The average (arithmetic mean) annual salary for teachers is

26, 000. I f t h eco l l e g e p a y s a t o t a l o f

3,380,000 in annual salaries to its teachers, how many students does the college have ?

505-555 (Easy)

A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

555-605 (Medium)

A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1 1 2 times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 50 hours?

605-655 (Medium)

A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)

605-655 (Medium)

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?

505-555 (Easy)

If a = 1 and (a - b)/c = 1 which of the following is NOT a possible value of b?

Sub 505 (Easy)

The table above show the daily change in the price of a certain stock last week. What was the net change in dollars in the price of the stock for the week?

555-605 (Medium)

1,234 1,243 1,324 ..... .... +4,321 The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers?

505-555 (Easy)

According to the table above, the number of fellows was approximately what percent of the total membership of Organization X?

505-555 (Easy)

One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?

Sub 505 (Easy)

Which of the following is equal to x 18 x 18 for all positive values of x ?

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