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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505-555 (Easy)

In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent, what is the denominator of the fraction?

605-655 (Medium)

The figure shows the graph of

y = (x + 1) (x - 1)^{2}

in the

x y

-plane. At how many points does the graph of

y = (x + 1) (x - 1)^{2} + 2

intercept the

x

-axis?

505-555 (Easy)

In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?

655-705 (Hard)

The cost to rent a small bus for a trip is

x

dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of

x

, will it cost per person?

555-605 (Medium)

If 0 < x < 1, what is the median of the values x , x − 1 , x 2 , x √ x and x 3 ?

655-705 (Hard)

Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

505-555 (Easy)

If a function f is defined by f (x) = − 1 x for all non zero numbers x. If f (a) = − 1 2 and f (a b) = 1 6 then b= ?

655-705 (Hard)

n

is a positive integer and the product of all the integers from 1 to

n

, inclusive, is divisible by 990, what is the least possible value of

n

Sub 505 (Easy)

A certain method for calculating pediatric drug dosages states that if d is the adult dosage, in milligrams, and y is the child’s age, in years, then the child’s dosage, in milligrams, is d × (y + 1 24) . If the adult dosage for a particular drug is 800 milligrams, what is an 8-year-old child’s dosage, in milligrams, according to this method?

655-705 (Hard)

The probability that event

M

will NOT occur is

0.8

and the probability that event

R

will NOT occur is

0.6

. If events

M

and

R

CANNOT both occur, which of the following is the probability that either event

M

or event

R

will occur?

Sub 505 (Easy)

Of the following, which is the closest to 60.2 1.03 * 4.86 ?

655-705 (Hard)

The total cost for Company X to produce a batch of tools is

$10, 000

plus

$3

per tool. Each tool sells for

$8

. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

Sub 505 (Easy)

The population of City X is 50 percent of the population of City Y. The population of City X is what percent of the total population of City X and City Y?

655-705 (Hard)

Q

is an odd number and the median of

Q

consecutive integers is 120, what is the largest of these integers?

Sub 505 (Easy)

The regular price per can of a certain brand of soda is $0.40. If the regular price per can is discounted 15 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases?

655-705 (Hard)

If there are fewer than 8 zeros between the decimal point and the first nonzero digit in the decimal expansion of

(\frac{t}{1 , 000})^{4}

, which of the following numbers could be the value of

t

? I. 3 II. 5 III. 9

Sub 505 (Easy)

If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

655-705 (Hard)

A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

Sub 505 (Easy)

To rent a tractor, it costs a total of x dollars for the first 24 hours, plus y dollars per hour for each hour in excess of 24 hours. Which of the following represents the cost, in dollars, to rent a tractor for 36 hours?

655-705 (Hard)

Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

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