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)

Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

655-705 (Hard)

How many prime numbers between

1

and

100

are factors of

7, 150

505-555 (Easy)

According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N (t) = − 20 (t − 5) 2 + 500 for 0 ≤ t ≤ 10 . According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?

655-705 (Hard)

A sequence of numbers

a_{1}, a_{2}, a_{3}, \dots

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

Sub 505 (Easy)

If the average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18, then N =

655-705 (Hard)

Last year the price per share of Stock X increased by

k

percent and the earnings per share of Stock X increased by

m

percent, where

k

is greater than

m

. By what percent did the ratio of price per share to earnings per share increase, in terms of

k

and

m

605-655 (Medium)

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

655-705 (Hard)

Of the

300

subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights,

40%

experienced sweaty palms,

30%

experienced vomiting, and

75%

experienced dizziness. If all of the subjects experienced at least one of these effects and

35%

of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

705-805 (Hard)

A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

655-705 (Hard)

m^{- 1} = - \frac{1}{3}

, then

m^{- 2}

is equal to

Sub 505 (Easy)

If mn ≠ 0 and 25 percent of n equals 37 1 2 percent of m, what is the value of 12 n m ?

655-705 (Hard)

A photography dealer ordered

60

Model X cameras to be sold for

$250

each, which represents a

20

percent markup over the dealer's initial cost for each camera. Of the cameras ordered,

6

were never sold and were returned to the manufacturer for a refund of

50

percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer's initial cost for the

60

cameras?

605-655 (Medium)

The table shows the amount budgeted and the amount spent for each of three accounts in a certain company.For which of these accounts did the amount spent differ from the amount budgeted by more than 6 percent of the amount budgeted ?

655-705 (Hard)

Seven pieces of rope have an average (arithmetic mean) length of

68

centimeters and a median length of

84

centimeters. If the length of the longest piece of rope is

14

centimeters more than

4

times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

Sub 505 (Easy)

If n = 20! + 17, then n is divisible by which of the following?

655-705 (Hard)

What is the difference between the sixth and the fifth terms of the sequence

2, 4, 7, \dots

whose

n^{th}

term is

n + 2^{n - 1}

Sub 505 (Easy)

A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?

655-705 (Hard)

From the consecutive integers

- 10

10

, inclusive,

20

integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the

20

integers?

605-655 (Medium)

Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

655-705 (Hard)

The letters D, G, I, I, and T can be used to form

5

-letter strings such as DIGIT or DGIIT. Using these letters, how many

5

-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?

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