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 x + 5y = 16 and x = -3y, then y =

505-555 (Easy)

A certain bakery has 6 employees. It pays annual salaries of

14, 000 t oe a c h o f 2 e m pl oy ees,

16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?

655-705 (Hard)

The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the lenght and width of the frame, what is the length of the picture, in inches?

505-555 (Easy)

If x and y are prime numbers, which of the following CANNOT be the sum of x and y?

Sub 505 (Easy)

What is the least integer that is a sum of three different primes each greater than 20 ?

Sub 505 (Easy)

A poll reveals that the average (arithmetic mean) income of 10 households is

25, 000. I f 6 o f t h e h o u se h o l d s ha v e in co m eso f

30,000 each, what is the average income of the other 4 households?

Sub 505 (Easy)

A company accountant estimates that airfares next year for business trips of a thousand miles or less will increase by 20 percent and airfares for all other business trips will increase by 10 percent. This year total airfares for business trips of a thousand miles or less were

9, 900 an d ai r f a r es f or a l l o t h er b u s in ess t r i p s w er e

13,000. According to the accountant's estimate, if the same number of business trips will be made next year as this year, how much will be spent for airfares next year?

555-605 (Medium)

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

Sub 505 (Easy)

A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold. Which of the following expresses this relationship ?

Sub 505 (Easy)

According to the graph above, what percent of the funds for highway maintenance came from the tax on tires?

505-555 (Easy)

If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^2 have?

Sub 505 (Easy)

If y= 4 + (x - 3)^2, then y is lowest when x =

555-605 (Medium)

Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?

Sub 505 (Easy)

90 − 8 (20 : 4) 1 2

Sub 505 (Easy)

If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

Sub 505 (Easy)

If 0 ≤ x ≤ 4 and y < 12 , which of the following CANNOT be the value of xy?

555-605 (Medium)

Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax. How much money could she have saved if she had bought the stereo at the same retail price in a neighboring state where she would have paid a sales tax of 5 percent?

Sub 505 (Easy)

If a 10 percent deposit that has been paid toward the purchase of a certain product is $110, how much more remains to be paid?

Sub 505 (Easy)

y = 248 - 398x Which of the following values of x gives the greatest value of y in the equation above?

Sub 505 (Easy)

All of the following have the same value EXCEPT?

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