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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555-605 (Medium)

Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

505-555 (Easy)

k

is a positive integer, what is the remainder when

(k + 2) (k^{3} - k)

is divided by

6

Sub 505 (Easy)

If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

505-555 (Easy)

Which of the following fractions is closest to

\frac{1}{2}

555-605 (Medium)

A manufacturer makes and sells 2 products, P and Q. The revenue from the sale of each unit of P is

20.00 an d t h er e v e n u e f r o m t h es a l eo f e a c h u ni t o f Q i s

17.00. Last year the manufacturer sold twice as many units of Q as P. What was the manufacturer’s average (arithmetic mean) revenue per unit sold of these 2 products last year?

505-555 (Easy)

p \neq = 0

and

p - \frac{1 - p ^{2}}{p} = \frac{r}{p}

, then

r =

A certain musical scale has 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 7th note in the scale is how many cycles per second?

505-555 (Easy)

\frac{∣ z ∣}{w} = 1

, which of the following must be true?

505-555 (Easy)

In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?

505-555 (Easy)

What number is

108

more than two-thirds of itself?

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?

505-555 (Easy)

A service provider charges

c

dollars for the first 50 hours of service used per month and 40 cents for each 30 minutes in excess of 50 hours used during the month. If

x

is an integer greater than 50, which of the following expressions gives this service provider’s charge, in dollars, for a month in which

x

hours of service were used?

505-555 (Easy)

Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?

505-555 (Easy)

A salesperson who had been driving at a speed of 100 kilometers per hour slowed down to a speed of 47 kilometers per hour. Approximately how many miles per hour was the speed reduced? (1 kilometer

\approx 0.625

mile)

605-655 (Medium)

Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members. This year the senate has the same number of members as last year, but it has 2 fewer Republican members than last year. If this year the number of Republican members is 2/3 the number of senate members, how many members does the senate have this year?

505-555 (Easy)

5 x - 8 = 12

and

x = y + 3

, then

y =

555-605 (Medium)

Kevin invested

8, 000 f or o n ey e a r a t a s im pl e ann u a l in t er es t r a t eo f 6 p er ce n t an d in v es t e d

10,000 for one year at an annual interest rate of 8 percent compounded semiannually. What is the total amount of interest that Kevin earned on the two investments?

505-555 (Easy)

The table above shows the numbers of hours of television programs that Jane recorded last week and the numbers of hours she spent viewing these recorded programs. No recorded program was viewed more than once. If

h

is the number of hours of recorded programs she had not yet viewed by the end of Friday, which of the following intervals represents all of the possible values of

h

555-605 (Medium)

The table shows partial results of a survey in which consumers were asked to indicate which one of six promotional techniques most influenced their decision to buy a new food product. Of those consumers who indicated one of the four techniques listed, what fraction indicated either coupons or store displays?

505-555 (Easy)

A dance troupe has a total of 50 dancers split into 2 groups. The costumes worn by Group A cost

$80

each, and those worn by Group B cost

$90

each. If the total cost of all the costumes is

$4, 270

, what is the total cost of the costumes worn by Group B?

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