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)

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?

655-705 (Hard)

Sixty percent of the members of a study group are women, and 45 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?

555-605 (Medium)

In the first week of the Year, Nancy saved

1. I n e a c h o f t h e n e x t 51 w ee k s, s h es a v e d

1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?

655-705 (Hard)

Each year for 4 years, a farmer increased the number of trees in a certain orchard by

\frac{1}{4}

of the number of trees in the orchard the preceding year. If all of the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period?

Sub 505 (Easy)

If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

655-705 (Hard)

According to the chart shown, which of the following is closest to the median annual number of shipments of manufactured homes in the United States for the years from 1990 to 2000, inclusive?

Sub 505 (Easy)

If the range of the six numbers 4, 3, 14, 7, 10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?

655-705 (Hard)

For the positive integers

a

b

, and

k

a^{k} ∥ b

means that

a^{k}

is a divisor of

b

, but

a^{k + 1}

is not a divisor of

b

. If

k

is a positive integer and

2^{k} ∥ 72

, then

k

is equal to

Sub 505 (Easy)

In a small snack shop, the average (arithmetic mean) revenue was

400 p er d a y o v er a 10 - d a y p er i o d . D u r in g t hi s p er i o d, i f t h e a v er a g e d ai l y r e v e n u e w a s

360 for the first 6 days, what was the average daily revenue for the last 4 days?

655-705 (Hard)

A certain characteristic in a large population has a distribution that is symmetric about the mean

m

. If 68 percent of the distribution lies within one standard deviation

d

of the mean, what percent of the distribution is less than

m + d

Sub 505 (Easy)

655-705 (Hard)

Four extra-large sandwiches of exactly the same size were ordered for

m

students, where

m > 4

. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

Sub 505 (Easy)

The total cost for Company X to produce a batch of tools is

10, 000 pl u s

3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is

655-705 (Hard)

Which of the following equations has

1 + 2

as one of its roots?

605-655 (Medium)

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

655-705 (Hard)

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?

605-655 (Medium)

If n = 3 8 - 2 8 , which of the following is NOT a factor of n?

655-705 (Hard)

In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?

Sub 505 (Easy)

If 5 − 6 x = x , then x has how many possible values?

655-705 (Hard)

At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?

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