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 x ≠ 3 and (x 2 − 9) 2 y = (x − 3) 4 , then in terms of y , x = ?

605-655 (Medium)

Each step of a staircase is 0.25 meter wide and 0.20 meter high, as shown in the figure above. All angles shown in the figure are right angles. If the height of the staircase is 3.6 meters and the landing at the top of the staircase is 1 meter wide, how long, in meters, is AB?

Sub 505 (Easy)

x 2 − (x 2) 2 =

505-555 (Easy)

The volume of a box with a square base is 54 cubic centimeters. If the height of the box is twice the width of the base, what is the height, in centimeters?

Sub 505 (Easy)

A digital wristwatch was set accurately at 8.30 am and then lost 2 seconds every 5 minutes. What time was indicated on the watch at 6.30 pm of the same day, if the watch operated continuously until that time?

Sub 505 (Easy)

On a purchase of

120, a s t or eo f f er e d a p a y m e n tpl an co n s i s t in g o f a

20 down payment and 12 monthly payments of $10 each. what percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?

505-555 (Easy)

At a special sale, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at this sale, the amount saved will be what percent of the original price of the 5 tickets?

Sub 505 (Easy)

How many of the integers between 25 and 45 are even?

Sub 505 (Easy)

If x y = 2 , then (x − y) y =

505-555 (Easy)

Three automobiles travel distances that are in the ratios of 1:2:3. If the ratios of the traveling times over these distances for these automobiles are 3:2:1 in the same respective order, what are the ratios of their respective average speeds?

Sub 505 (Easy)

A person bought a ticket to a ball game for

15 an d l a t er so l d t h e t i c k e t f or

60. What was the percent increase in the price of the ticket?

Sub 505 (Easy)

In the figure above, what is the value of 2x - y?

Sub 505 (Easy)

A national travel survey in 1977 found that Americans took 382.6 million trips within the United States. California was the destination of 38 million trips. Approximately what percent of the trips had California as the destination?

Sub 505 (Easy)

In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 8 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?

505-555 (Easy)

In the figure above, two rectangles with the same dimensions overlap to form the shaded region. If each rectangle has perimeter 12 and the shaded region has perimeter 3, what is the perimeter of the resulting figure?

555-605 (Medium)

The figure above shows the shape of a sign to be placed in front of a flower store. The sign has a semicircle on each side of the square. If the sign is 3 centimeters thick and if each side of the square is 50 centimeters long, what is the volume, in cubic centimeters, of the sign?

Sub 505 (Easy)

Audrey went shopping with D dollars. She spent 20% of her money on a blouse and 25% of what was left on a pair of shoes. What per cent of the original D dollars did she spend?

555-605 (Medium)

In the figure above, the five circles have points in common as shown. P is the center of the largest circle, Q and R are centers of the medium-sized circles, and Q, P, and R are points on a straight line. What fraction of the largest circular region is shaded?

Sub 505 (Easy)

If x > 0 and x 2 = 161 , what is the best whole number approximation of x ?

505-555 (Easy)

The number of diagonals of a polygon of n sides is given by the formula d=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?

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