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)

If 65 percent of a certain firm’s employees are full-time and if there are 5,100 more full-time employees than part-time employees, how many employees does the firm have?

605-655 (Medium)

Four identical machines can produce

x

units in 6 days. How many can produce

3 x

units in 4 days at the same rate?

505-555 (Easy)

At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

605-655 (Medium)

The symbol

Δ

denotes addition, subtraction, multiplication, or division. If

6Δ3 \leq 3

, which must be true? I.

2Δ2 = 0

II.

2Δ2 = 1

III.

4Δ2 = 2

505-555 (Easy)

For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?

605-655 (Medium)

mn \neq = 0

and 25 percent of

n

equals

37 \frac{1}{2}

percent of

m

, what is the value of

\frac{12 n}{m}

505-555 (Easy)

Set X consists of eight consecutive integers. Set Y consists of all the integers that result from adding 4 to each of the integers in set X and all the integers that result from subtracting 4 from each of the integers in set X. How many more integers are there in set Y than in set X ?

605-655 (Medium)

N

and

M

are each 3-digit integers. Each of 1, 2, 3, 6, 7, and 8 is a digit of either

N

M

. What is the smallest possible positive difference between

N

and

M

605-655 (Medium)

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)

The table shows partial results of a survey in which consumers selected one of six promotional techniques. Of those who indicated one of the four techniques listed, what fraction indicated either coupons or store displays?

Sub 505 (Easy)

Last week Chris earned x dollars per hour for the first 40 hours worked plus 22 dollars per hour for each hour worked beyond 40 hours. If last week Chris earned a total of 816 dollars by working 48 hours, what is the value of x ?

605-655 (Medium)

If 65 percent of a firm’s employees are full-time and there are 5,100 more full-time employees than part-time employees, how many employees does the firm have?

555-605 (Medium)

The sides of each of two plastic cubes are numbered 1 through 6, and each number is equally likely to appear face up after either cube is rolled. What is the probability that, after the two cubes are rolled, the sum of the two numbers appearing face up will be greater than 9?

605-655 (Medium)

The cost

C

, in dollars, to remove

p

percent of a pollutant is

C = \frac{100 , 000 p}{100 - p}

. How much more would it cost to remove 90 percent than 80 percent?

655-705 (Hard)

If there are fewer than 8 zeroes between the decimal point and the first nonzero digit in the decimal expansion of (t 1000) 4 , which of the following numbers could be the value of t?

605-655 (Medium)

x y \neq = 0

and

x^{2} y^{2} - x y = 6

, which could be

y

in terms of

x

? I.

\frac{1}{2 x}

II.

- \frac{2}{x}

III.

\frac{3}{x}

Sub 505 (Easy)

What is the remainder of 3^19 when divided by 10?

605-655 (Medium)

If the positive number

d

is the standard deviation of

n, k,

and

p

, then the standard deviation of

n + 1, k + 1,

and

p + 1

505-555 (Easy)

An auction house charges a commission of 15% on the first

50, 000 o f t h es a l e p r i ceo f ani t e m, pl u s 10

50,000. What was the price of a painting for which the house charged a total commission of $24,000?

605-655 (Medium)

In a high school, 80 percent of seniors take calculus, and 60 percent of calculus students also take physics. If 10 percent take neither calculus nor physics, what percent take physics?

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