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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Sub 505 (Easy)

The value of 7 8 + 1 9 1 2 is closest to which of the following?

655-705 (Hard)

Which of the following is equivalent to the pair of inequalities

x + 6 > 10

and

x - 3 \leq 5

Sub 505 (Easy)

Which of the following expressions can be written as an integer?

655-705 (Hard)

David has

d

books, which is 3 times as many as Jeff and

\frac{1}{2}

as many as Paula. How many books do the three of them have altogether, in terms of

d

505-555 (Easy)

Which of the following is greatest?

655-705 (Hard)

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

Sub 505 (Easy)

(1/2) − 3 (1/4) − 2 (1/16) − 1 = (1/2) − 3 (1/4) − 2 (1/16) − 1 =

655-705 (Hard)

At his regular hourly rate, Don had estimated the labor cost of a repair job as

$336

and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned

$2

per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

655-705 (Hard)

If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is

655-705 (Hard)

\frac{p}{q} < 1

, and

p

and

q

are positive integers, which of the following must be greater than 1?

505-555 (Easy)

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

655-705 (Hard)

To mail a package, the rate is

x

cents for the first pound and

y

cents for each additional pound, where

x > y

. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

555-605 (Medium)

How many prime numbers between 1 and 100 are factors of 7,150?

655-705 (Hard)

If money is invested at

r

percent interest, compounded annually, the amount of the investment will double in approximately

\frac{70}{r}

years. If Pat’s parents invested

$5, 000

in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

505-555 (Easy)

The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w?

655-705 (Hard)

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy’s car got on this trip must have been between

The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly 1/2 centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum volume?

655-705 (Hard)

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

505-555 (Easy)

If x/y = c/d and d/c = b/a, which of the following must be true?

655-705 (Hard)

In a small snack shop, the average (arithmetic mean) revenue was

$400

per day over a 10-day period. During this period, if the average daily revenue was

$360

for the first 6 days, what was the average daily revenue for the last 4 days?

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