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)

What is the smallest integer n for which 25^n > 5^12 ?

655-705 (Hard)

A pharmaceutical company received

$3

million in royalties on the first

$20

million in sales of the generic equivalent of one of its products and then

$9

million in royalties on the next

$108

million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first

$20

million in sales to the next

$108

million in sales?

Sub 505 (Easy)

If s > 0 and r s √ = s , what is r in terms of s ?

655-705 (Hard)

The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room. Thus, after someone enters or exits the room, the light remains on for only 15 minutes unless the door opens again and resets the timer for another 15 minutes. If the times listed above are the times at which the door opened from 8:00 to 10:00, approximately how many minutes during this two-hour period was the light off?

505-555 (Easy)

Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January?

655-705 (Hard)

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

Sub 505 (Easy)

Last year Joe grew 1 inch and Sally grew 200 percent more than Joe grew. How many inches did Sally grow last year?

655-705 (Hard)

n = 3^{8} - 2^{8}

, which of the following is NOT a factor of

n

Sub 505 (Easy)

If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?

655-705 (Hard)

Club X has more than 10 but fewer than 40 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?

Sub 505 (Easy)

A store reported total sales of

385 mi l l i o n f or F e b r u a r y o f t hi sy e a r . I f t h e t o t a l s a l es f or t h es am e m o n t h l a s t y e a r w a s

320 million, approximately what was the percent increase in sales?

655-705 (Hard)

In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?

655-705 (Hard)

If d = 1 2 3 * 5 7 is expressed as a terminating decimal, how many nonzero digits will d have?

655-705 (Hard)

s > 0

and

\frac{r}{s} = s

, what is

r

in terms of

s

505-555 (Easy)

If [x] is the greatest integer less than or equal to x, what is the value of [-1.6] + [3.4] + [2.7]?

655-705 (Hard)

3 < x < 100

, for how many values of

x

\frac{x}{3}

the square of a prime number?

605-655 (Medium)

The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?

655-705 (Hard)

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?

605-655 (Medium)

Which of the following fractions is closest to 1 2 1 2 ?

655-705 (Hard)

An object thrown directly upward is at a height of

h

feet after

t

seconds, where

h = - 16 (t - 3)^{2} + 150

. At what height, in feet, is the object 2 seconds after it reaches its maximum height?

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