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)

When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

505-555 (Easy)

k^{2} = m^{2}

, which of the following must be true?

Sub 505 (Easy)

David has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?

505-555 (Easy)

Makoto, Nishi, and Ozuro were paid a total of

$780

for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?

555-605 (Medium)

Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

505-555 (Easy)

x

is a positive integer and

4^{x} - 3 = y

, which of the following CANNOT be a value of

y

555-605 (Medium)

If M = √ 4 + 3 √ 4 + 4 √ 4 M = 4 √ + 4 √ 3 + 4 √ 4 , then the value of M is:

505-555 (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?

505-555 (Easy)

The value of 2 (− 14) + 2 (− 15) + 2 (− 16) + 2 (− 17) 5 is how many times the value of 2 (− 17) ?

505-555 (Easy)

The quotient when a certain number is divided by

\frac{2}{3}

\frac{9}{2}

. What is the number?

555-605 (Medium)

In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?

505-555 (Easy)

The price of gasoline at a service station increased from

$1.65

per gallon last week to

$1.82

per gallon this week. Sally paid

$26.40

for gasoline last week at the station. How much more will Sally pay this week at the station for the same amount of gasoline?

555-605 (Medium)

Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

505-555 (Easy)

Harry spent

25%

of his

$2, 200

May take-home pay on rent and

30%

of the remainder on food. How much of his May take-home pay did Harry spend on food?

Sub 505 (Easy)

If x is a positive integer and 4 x – 3 = y , which of the following CANNOT be a value of y ?

505-555 (Easy)

2 x + y = 7

and

x + 2 y = 5

, then

\frac{x + y}{3} =

Sub 505 (Easy)

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

505-555 (Easy)

City

X

has a population 4 times as great as the population of City

Y

, which has a population twice as great as the population of City

Z

. What is the ratio of the population of City

X

to the population of City

Z

Sub 505 (Easy)

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?

505-555 (Easy)

According to the table above, the number of fellows was approximately what percent of the total membership of Organization

X

? Note: All categories of membership are mutually exclusive.

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