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)

If 3x + 2y = 36 and x + y = 14, what is the value of x?

505-555 (Easy)

If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?

505-555 (Easy)

In the graduating class of a certain college,

48%

of the students identify exclusively as male and

52%

identify exclusively as female. In this class,

40%

of the students who identify as male and

20%

of the students who identify as female are 25 years old or older. If one student in the graduating class is randomly selected, approximately what is the probability that the student will be less than 25 years old?

605-655 (Medium)

A mixture contains 30 litres of juice and water in the ratio 2 : 3. How many litres of juice must be added to make the ratio 1 : 1?

Sub 505 (Easy)

As a salesperson, Phyllis can choose one of two methods of annual payment: either an annual salary of

35, 000 w i t hn oco mmi ss i o n or anann u a l s a l a r y o f

10,000 plus a 20 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

505-555 (Easy)

In a certain board game, a stack of 48 cards, 8 of which represent a single share of stock, are shuffled and then placed face down. If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

505-555 (Easy)

If the average of five consecutive integers is 14, what is the largest of them?

Sub 505 (Easy)

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

505-555 (Easy)

During a trip that they took together, Carmen, Juan, Maria, and Rafael drove an average (arithmetic mean) of 80 miles each. Carmen drove 72 miles, Juan drove 78 miles, and Maria drove 83 miles. How many miles did Rafael drive?

505-555 (Easy)

A circle has an area of 49π. What is its circumference?

Sub 505 (Easy)

In a certain baord game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down. If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

505-555 (Easy)

Each week, a clothing salesperson receives a commission equal to

15%

of the first

$500

in sales and

20%

of all additional sales that week. What commission would the salesperson receive on total sales for the week of

$1, 300

605-655 (Medium)

How many different 3-letter arrangements can be formed from the letters of the word "MATH" without repeating any letter?

Sub 505 (Easy)

Each week, a clothing salesperson receives a commission equal to 15 percent of the first

500 in s a l es an d 20 p er ce n t o f a l l a dd i t i o na l s a l es t ha tw ee k . W ha t co mmi ss i o n w o u l d t h es a l es p er so n r ece i v eo n t o t a l s a l es f or t h e w ee k o f

1,300 ?

505-555 (Easy)

Five batches of 100 nails each are taken from a production line. The numbers of defective nails in the first four batches are 2, 4, 3, and 5, respectively. If the fifth batch has either 1, 2, or 6 defective nails, for which of these values does the average (arithmetic mean) number of defective nails per batch for the five batches equal the median number of defective nails for the five batches? I.

1

II.

2

III.

6

605-655 (Medium)

If 0 < x < 1, which of the following must be greatest?

605-655 (Medium)

The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

505-555 (Easy)

List

S

consists of 10 consecutive odd integers, and list

T

consists of 5 consecutive even integers. If the least integer in

S

is 7 more than the least integer in

T

, how much greater is the average (arithmetic mean) of the integers in

S

than the average of the integers in

T

605-655 (Medium)

A store offers a 20% discount on a jacket that originally costs $80. A 10% sales tax is applied to the discounted price. What is the final price paid by the customer?

505-555 (Easy)

Over the past 7 weeks, the Smith family had weekly grocery bills of

74,

69,

64,

79,

64,

84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7-week period?

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