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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555-605 (Medium)

A pharmaceutical company received

3 mi l l i o nin r oy a l t i eso n t h e f i r s t

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

9 mi l l i o nin r oy a l t i eso n t h e n e x t

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

20 mi l l i o nin s a l es t o t h e n e x t

108 million in sales?

505-555 (Easy)

125%

5 =

555-605 (Medium)

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?

505-555 (Easy)

Each day Linda spends 6 hours at her dog-walking job, for which she is paid

$15.00

per hour. In addition, Linda spends a total of 1.5 hours each day, for which she is not paid, traveling to and from the job. What is Linda's hourly rate of pay for the total amount of time that she spends each day at her dog-walking job and traveling to and from that job?

555-605 (Medium)

If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X?

505-555 (Easy)

When traveling at a constant speed of 32 miles per hour, a certain motorboat consumes 24 gallons of fuel per hour. What is the fuel consumption of this boat at this speed measured in miles traveled per gallon of fuel?

605-655 (Medium)

If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y, where X and Y are nonzero digits, which of the following is closest to the greatest possible value of 0.1 X 0.02 Y ?

505-555 (Easy)

If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter?

Sub 505 (Easy)

Which of the following is equal to the average (arithmetic mean) of (x + 2)^2 and (x - 2)^2?

505-555 (Easy)

From 2000 to 2003, the number of employees at a certain company increased by a factor of

\frac{1}{4}

. From 2003 to 2006, the number of employees at this company decreased by a factor of

\frac{1}{3}

. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000?

505-555 (Easy)

If the units digit of 5 , 610.37 10 k is 6, what is the value of k?

505-555 (Easy)

Working alone at its own constant rate, machine

R

fills 10,000 boxes with pins in 9 hours, and working alone at its own constant rate, machine

S

fills 5,000 boxes with pins in 3 hours. If machine

R

and machine

S

, each working at its own constant rate and for the same period of time, together filled a certain number of boxes with pins, what percent of the boxes were filled by machine

R

655-705 (Hard)

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

336 an d h e w a s p ai d t ha t am o u n t . H o w e v er, t h e j o b t oo k 4 h o u r s l o n g er t hanh e ha d es t ima t e d an d, co n se q u e n tl y, h ee a r n e d

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

505-555 (Easy)

A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of

$2.35

. How many of the coins have a face value of 25 cents?

655-705 (Hard)

A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer n is divisible by 3, and n is of the form 1k2,k24, where k represents a digit that occurs twice, how many values could k have?

505-555 (Easy)

A retailer purchased eggs at

$2.80

per dozen and sold the eggs at 3 eggs for

$0.90

. What was the retailer's gross profit from purchasing and selling 5 dozen eggs? (1 dozen eggs = 12 eggs)

Sub 505 (Easy)

In the table above, what is the number of green marbles in Jar R ?

505-555 (Easy)

In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24. One card will be drawn at random from the set. What is the probability that the card drawn will have either a number that is divisible by both 2 and 3 or a number that is divisible by 7?

605-655 (Medium)

List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T?

505-555 (Easy)

As a salesperson, Phyllis can choose one of two methods of annual payment: either an annual salary of

$35, 000

with no commission or an annual salary of

$10, 000

plus a

20%

commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

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