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 p ≠ 0 and p – (1 – p 2) p = r p , then r =

605-655 (Medium)

A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

505-555 (Easy)

In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?

605-655 (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

? (1 kilometer = 1,000 meters)

Sub 505 (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?

605-655 (Medium)

The function

f

is defined by

f (x) = - \frac{1}{x}

for all nonzero numbers

x

. If

f (a) = - \frac{1}{2}

and

f (ab) = \frac{1}{6}

, then

b =

505-555 (Easy)

Sam has

800 inhi s a cco u n t . H e w i l l d e p os i t

1 in his account one week from now,

2 tw o w ee k s f r o mn o w, an d e a c h w ee k t h er e a f t er h e w i l l d e p os i t anam o u n tt ha t i s

1 greater than the amount that he deposited one week before. If there are no other transactions, how much money will Sam have in his account 50 weeks from now?

605-655 (Medium)

5^{x} - 5^{x - 3} = (124) (5^{y})

, what is

y

in terms of

x

505-555 (Easy)

If each of the 12 teams participating in a certain tournament plays exactly one game with each of the other teams, how many games will be played?

605-655 (Medium)

The total of Company C’s assets in 1994 was 300 percent greater than the total in 1993, which in turn was 400 percent greater than the total in 1992. If the total of Company C’s assets in 1992 was

N

dollars, which of the following represents the total of Company C’s assets, in dollars, in 1994?

555-605 (Medium)

The table above shows the distribution of the number of absences from a certain English class during the spring semester. For those students who had at least 1 absence, what was the median number of absences?

605-655 (Medium)

\frac{x}{∣ y ∣} = - 1

, which of the following must be true?

555-605 (Medium)

If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

605-655 (Medium)

The table above is a 3 by 3 grid of 9 numbers, 5 of which are given. The 4 numbers that are not given are denoted by

A

B

C

, and

D

. The product of the numbers in each row and in each column is the same for all rows and columns. What is the value of the product

A B C D

Sub 505 (Easy)

A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost

80 e a c h, an d t h ose w or nb y G r o u pB cos t

90 each. If the total cost of all the costumes is $4,270, what is the total cost of the costumes worn by Group B ?

605-655 (Medium)

In May, Mrs. Lee’s earnings were 60 percent of the Lee family’s total income. In June, Mrs. Lee earned 20 percent more than in May. If the rest of the family’s income was the same both months, then in June, Mrs. Lee’s earnings were approximately what percent of the Lee family’s total income?

Sub 505 (Easy)

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?

605-655 (Medium)

John would have reduced the time it took him to drive from his home to a certain store by

\frac{1}{3}

if he had increased his average speed by 15 miles per hour. What was John’s actual average speed, in miles per hour, when he drove from his home to the store?

555-605 (Medium)

The graph shows the number of computers assembled during each of 6 consecutive days. From what day to the next day was the percent change in the number of computers assembled the greatest in magnitude ?

605-655 (Medium)

Which of the following inequalities has a solution set that, when graphed on a number line, is a single line segment of finite length?

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