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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605-655 (Medium)

After paying a 10 percent tax on all income over

3, 000, a p er so nha d an e t in co m eo f

12,000. What was the income before taxes?

655-705 (Hard)

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

555-605 (Medium)

How many three-digit numerals begin With a digit that represents a prime number and end with a digit that represents a prime number?

505-555 (Easy)

If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?

Sub 505 (Easy)

(− 1) 2 − (− 1) 3 =

505-555 (Easy)

Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?

505-555 (Easy)

If r = 1 + 1 3 + 1 9 + 1 27 and s = 1 + 1 3 r , then s exceeds r by

555-605 (Medium)

The average (arithmetic mean) of 3 different positive integers is 100 and the largest of these 3 integers is 120. What is the least possible value of the smallest of these 3 integers?

555-605 (Medium)

If 0.497 mark has the value of one dollar, what is the value to the nearest dollar of 350 marks?

655-705 (Hard)

There are 4 card-processing machines in an office. The fastest of these machines processes x cards in 7 hours and the slowest processes x cards in 8 hours. Which of the following could NOT be the average time per machine for each of the 4 machines to process x cards?

605-655 (Medium)

A decorator bought a bolt of defective cloth that he judged to be 3/4 usable, in which case the cost would be $0.80 per usable yard. If it was later found that only 2/3 of the bolt could be used, what was the actual cost per usable yard?

Sub 505 (Easy)

If x ≠ 0, 2x = 5y, and 3z = 7x, what is the ratio of z to y?

Sub 505 (Easy)

Of a group of people surveyed in a political poll, 60 percent said that they would vote for candidate R. Of those who said they would vote for R, 90 percent actually voted for R, and of those who did not say that they would vote for R, 5 percent actually voted for R. What percent of the group voted for R?

505-555 (Easy)

In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?

555-605 (Medium)

How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?

555-605 (Medium)

In a student body the ratio of men to women was 1 to 4. After 140 additional men were admitted, the ratio of men to women became 2 to 3. How large was the student body after the additional men were admitted?

Sub 505 (Easy)

When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.5 centimeter. The actual diameter of the tissue, in centimeters, is

505-555 (Easy)

How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

555-605 (Medium)

An even number x divided by 7 gives some quotient plus a remainder of 6. Which of the following, when added to x, gives a sum which must be divisible by 14?

Sub 505 (Easy)

When the integer n is divided by 6, the remainder is 3, Which of the following is NOT a multiple of 6?

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