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)

If x^2 − 2 < 0, which of the following specifies all the possible values of x?

655-705 (Hard)

\frac{0.99999999}{1.0001} - \frac{0.99999991}{1.0003} =

605-655 (Medium)

Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

655-705 (Hard)

Last Sunday a certain store sold copies of Newspaper A for

$1.00

each and copies of Newspaper B for

$1.25

each, and the store sold no other newspapers that day. If

r

percent of the store's revenue from newspaper sales was from Newspaper A and if

p

percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses

r

in terms of

p

Sub 505 (Easy)

Abdul, Barb, and Carlos all live on the same straight road, on which their school is also located. The school is halfway between Abdul’s house and Barb’s house. Barb’s house is halfway between the school and Carlos’s house. If the school is 4 miles from Carlos’s house, how many miles is Abdul’s house from Carlos’s house?

655-705 (Hard)

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

Sub 505 (Easy)

While a family was away on vacation, they paid a neighborhood boy

11 p er w ee k t o m o w t h e i r l a w nan d

4 per day to feed and walk their dog. If the family was away for exactly 3 weeks, how much did they pay the boy for his services?

655-705 (Hard)

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by

27

. By how much do the two digits differ?

Sub 505 (Easy)

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?

655-705 (Hard)

In an electric circuit, two resistors with resistances

x

and

y

are connected in parallel. In this case, if

r

is the combined resistance of these two resistors, then the reciprocal of

r

is equal to the sum of the reciprocals of

x

and

y

. What is

r

in terms of

x

and

y

Sub 505 (Easy)

If z ≠ 0 and z + 1 − 2 z 2 z = w z , then w =

655-705 (Hard)

Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are

\frac{1}{4}

\frac{1}{2}

, and

\frac{5}{8}

, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

Sub 505 (Easy)

For the positive numbers, n, n + 1, n + 2, n + 4, and n + 8, the mean is how much greater than the median?

655-705 (Hard)

\frac{1}{x} - \frac{1}{x + 1} = \frac{1}{x + 4}

, then

x

could be

Sub 505 (Easy)

Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 47 percent were employees. What percent were stockholders, who were not employees?

655-705 (Hard)

(\frac{1}{2})^{- 3} (\frac{1}{4})^{- 2} (\frac{1}{16})^{- 1} =

555-605 (Medium)

For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball?

655-705 (Hard)

List

T

consists of

30

positive decimals, none of which is an integer, and the sum of the

30

decimals is

S

. The estimated sum of the

30

decimals,

E

, is defined as follows. Each decimal in

T

whose tenths digit is even is rounded up to the nearest integer, and each decimal in

T

whose tenths digit is odd is rounded down to the nearest integer;

E

is the sum of the resulting integers. If

\frac{1}{3}

of the decimals in

T

have a tenths digit that is even, which of the following is a possible value of

E - S

? I.

- 16

II.

6

III.

10

Sub 505 (Easy)

Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine door. However, Cheryl was given a discount of 25% off the regular price of each solid oak door. If the regular price of each hollow pine door was $40, what was the total price of all 11 doors?

655-705 (Hard)

5 - \frac{6}{x} = x

, then

x

has how many possible values?

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