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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555-605 (Medium)

If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

505-555 (Easy)

Positive integer y is 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?

Sub 505 (Easy)

If n = 16 81 − √ n = 16 81 , what is the value of n √ n ?

555-605 (Medium)

Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

Sub 505 (Easy)

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

605-655 (Medium)

A closed cylindrical tank contains 36 π cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

555-605 (Medium)

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

655-705 (Hard)

When the figure above is cut along the solid lines, folded along the dashed lines, and taped along the solid lines, the result is a model of a geometric solid. This geometric solid consists of 2 pyramids each with a square base that they share. What is the sum of number of edges and number of faces of this geometric solid?

555-605 (Medium)

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

Sub 505 (Easy)

4.8 * 10 9 − − − − √ 4.8 * 10 9 is closest in value to

655-705 (Hard)

In the figure shown, what is the value of v+x+y+z+w?

505-555 (Easy)

Solution X is 15% salt and solution Y is 50% salt. If the two solutions are combined to form 7 gallons of a 30% solution, how many gallons of solution X must be used?

Sub 505 (Easy)

A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?

555-605 (Medium)

If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?

505-555 (Easy)

A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

555-605 (Medium)

AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 4:00 P.M. x grams 7:00 P.M. 14.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?

Sub 505 (Easy)

If 893 × 78 = p, which of the following is equal to 893 × 79?

655-705 (Hard)

What is the tenths digit of the quotient when thirty-five hundredths is divided by four thousandths?

Sub 505 (Easy)

If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?

555-605 (Medium)

Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 32 laps around the track per hour and Nick completes 12 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?

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