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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505-555 (Easy)

The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

655-705 (Hard)

A furniture dealer purchased a desk for

$150

and then set the selling price equal to the purchase price plus a markup that was

40

percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?

555-605 (Medium)

Judy bought a quantity of pens in packages of 5 for

0.80 p er p a c k a g e . S h eso l d a l l o f t h e p e n s in p a c k a g eso f 3 f or

0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

655-705 (Hard)

How many odd numbers between

10

and

1, 000

are the squares of integers?

Sub 505 (Easy)

The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents , how many degrees of the circle should be used to represent an item that is 15 percent of the budget?

655-705 (Hard)

Three grades of milk are

1

percent,

2

percent, and

3

percent fat by volume. If

x

gallons of the

1

percent grade,

y

gallons of the

2

percent grade, and

z

gallons of the

3

percent grade are mixed to give

x + y + z

gallons of a

1.5

percent grade, what is

x

in terms of

y

and

z

Sub 505 (Easy)

If k^2 = m^2, which of the following must be true?

655-705 (Hard)

There are

8

books on a shelf, of which

2

are paperbacks and

6

are hardbacks. How many possible selections of

4

books from this shelf include at least one paperback?

Sub 505 (Easy)

A certain restaurant that regularly advertises through the mail has 1,040 cover letters and 3,000 coupons in stock. In its next mailing, each envelope will contain 1 cover letter and 2 coupons. If all of the cover letters in stock are used, how many coupons will remain in stock after this mailing?

655-705 (Hard)

M = 4 + 34 + 44

, then the value of

M

Sub 505 (Easy)

In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?

655-705 (Hard)

When a certain tree was first planted, it was

4

feet tall, and the height of the tree increased by a constant amount each year for the next

6

years. At the end of the

6^{th}

year, the tree was

\frac{1}{5}

taller than it was at the end of the

4^{th}

year. By how many feet did the height of the tree increase each year?

505-555 (Easy)

From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000 ?

655-705 (Hard)

A certain musical scale has

13

notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the

12

lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is

440

cycles per second, then the frequency of the seventh note in the scale is how many cycles per second?

Sub 505 (Easy)

When traveling at a constant speed of 32 miles per hour, a certain motorboat consumes 24 gallons of fuel per hour. What is the fuel consumption of this boat at this speed measured in miles traveled per gallon of fuel?

Sub 505 (Easy)

A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed?

Sub 505 (Easy)

If 1 < x < y < z, which of the following has the greatest value?

505-555 (Easy)

If k is an integer and (.0025)(.025)(.00025)10^k is an integer, what is the least possible value of K?

Sub 505 (Easy)

The sum of the weekly salaries of 5 employees is $3,250. If each of the 5 salaries is to increase by 10 percent, then the average (arithmetic mean) weekly salary per employee will increase by

505-555 (Easy)

A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order?

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