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:203050
If 3 < x < 100, for how many values of x is x/3 the square of a prime number?
505-555 (Easy)
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of body weight, by what percent was the prescribed dosage greater than the typical dosage?
505-555 (Easy)
If 5 x – 5 (x − 3) = 124 * 5 y , what is y in terms of x?
505-555 (Easy)
The function f is defined by f(x)=x−10 for all positive numbers x. If u=f(t) for some positive numbers t and u, what is t in terms of u?
605-655 (Medium)
In Country C, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
505-555 (Easy)
If 35% of a number is decreased by 15, then the result is 25% of the original number. What is the original number?
505-555 (Easy)
The profit P, in dollars, for any given month at a certain company is defined by P= I − C, where I represents total income, in dollars, and C represents total costs, in dollars, for the month. For each of the first 4 months of the year, C = I + 32,000; and for each of the next 3 months, I = C + 36,000. If I = C + 10,000 for each of the 5 remaining months of the year, what was the company's total profit for the 12-month year?
505-555 (Easy)
A flower arrangement consists of 30 roses, each of which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?
505-555 (Easy)
If the mass of 1 cubic centimeter of a certain substance is 7.3 grams, what is the mass, in kilograms, of 1 cubic meter of this substance?
505-555 (Easy)
Sixty percent of the people who responded to a company’s advertisement for a job opening were interviewed over the phone. Twenty percent of those interviewed over the phone, that is, 3 people, were asked to come to the company for a personal interview. How many people responded to the advertisement?
Sub 505 (Easy)
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation (a , b , c) Θ (d , e , f) = a d + b e + c f . What is the value of (1 , − 2 , 3) Θ (1 , − 1 2 , 1 3) (1 , − 2 , 3) Θ (1 , − 1 2 , 1 3) ?
505-555 (Easy)
(−3)−2=
655-705 (Hard)
A sequence of numbers a 1 , a 2 , a 3 ,.... is defined as follows: a 1 = 3 , a 2 = 5 , and every term in the sequence after a 2 is the product of all terms in the sequence preceding it, e.g, a 3 = (a 1) (a 2) and a 4 = (a 1) (a 2) (a 3) . If a n = t and n > 2 , what is the value of a n + 2 in terms of t?
505-555 (Easy)
Mark bought a set of 6 flowerpots 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?
655-705 (Hard)
Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?
505-555 (Easy)
If r and s are positive integers and r−s=6, which of the following has the greatest value?
555-605 (Medium)
If n = 33 43 + 43 33 what is the units digit of n?
505-555 (Easy)
An auction house charges a commission of 15 percent on the first $50,000 of the sale price of an item, plus 10 percent on the amount of the sale price in excess of $50,000. What was the sale price of a painting for which the auction house charged a total commission of $24,000?
555-605 (Medium)
In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?
505-555 (Easy)
At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?