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)

Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

655-705 (Hard)

Seed mixture X is

40

percent ryegrass and

60

percent bluegrass by weight; seed mixture Y is

25

percent ryegrass and

75

percent fescue. If a mixture of X and Y contains

30

percent ryegrass, what percent of the weight of the mixture is X?

555-605 (Medium)

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

655-705 (Hard)

How many of the integers that satisfy the inequality

\frac{( x + 2 ) ( x + 3 )}{x - 2} \geq 0

are less than

5

505-555 (Easy)

A bicycle store purchased two bicycles, one for

250 an d t h eo t h er f or

375, and sold both bicycles at a total gross profit of

250. I f t h es t or eso l d o n eo f t h e bi cy c l es f or

450, which of the following could be the store's gross profit from the sale of the other bicycle?

655-705 (Hard)

Of the

150

houses in a certain development,

60

percent have air-conditioning,

50

percent have a sunporch, and

30

percent have a swimming pool. If

5

of the houses have all three of these amenities and

5

have none of them, how many of the houses have exactly two of these amenities?

555-605 (Medium)

Greg assembles units of a certain product at a factory. Each day he is paid

2.00 p er u ni t f or t h e f i r s t 40 u ni t s t ha t h e a sse mb l es an d

2.50 for each additional unit that he assembles that day. If Greg assembled at least 30 units on each of two days and was paid a total of $180.00 for assembling units on the two days, what is the greatest possible number of units that he could have assembled on one of the two days?

655-705 (Hard)

The value of

\frac{2 ^{- 14} + 2 ^{- 15} + 2 ^{- 16} + 2 ^{- 17}}{5}

is how many times the value of

2^{- 17}

505-555 (Easy)

Carol purchased one basket of fruit consisting of 4 Apples and 2 Oranges and another basket of fruit consisting of 3 Apples and 5 Oranges. Carol is to select one piece of fruit at random from each of the two baskets. What is the probability that one of the two pieces of fruit selected will be an apple and the other will be an orange?

655-705 (Hard)

Which of the following fractions has a decimal equivalent that is a terminating decimal?

Sub 505 (Easy)

If (1 – 1.25)N = 1, then N =

655-705 (Hard)

(\frac{1}{5})^{m} (\frac{1}{4})^{18} = \frac{1}{2 ( 10 ) ^{35}}

, then

m =

505-555 (Easy)

If (1 3 + 1 4 + 1 5 + 1 6) = r (1 9 + 1 12 + 1 15 + 1 18) , then r =

655-705 (Hard)

From a group of

8

volunteers, including Andrew and Karen,

4

people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the

4

volunteers selected and Karen will not?

555-605 (Medium)

A worker carries jugs of liquid soap from a production line to a packing area, carrying 4 jugs per trip. If the jugs are packed into cartons that hold 7 jugs each, how many jugs are needed to fill the last partially filled carton after the worker has made 17 trips?

655-705 (Hard)

An investor purchased

100

shares of Stock X at

6 \frac{1}{18}

dollars per share and sold them all a year later at

24

dollars per share. If the investor paid a

2

percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

505-555 (Easy)

The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ?

655-705 (Hard)

x

is the product of the integers from

1

150

, inclusive, and

5^{y}

is a factor of

x

, what is the greatest possible value of

y

Sub 505 (Easy)

In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

655-705 (Hard)

The number of defects in the first five cars to come through a new production line are

9, 7, 10, 4,

and

6

, respectively. If the sixth car through the production line has either

3, 7,

12

defects, for which of these values does the mean number of defects per car for the first six cars equal the median? I.

3

II.

7

III.

12

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