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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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, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?

505-555 (Easy)

The table shows the numbers of packages shipped daily by each of five companies during a 4-day period. The standard deviation of the numbers of packages shipped daily during the period was greatest for which of the five companies?

Last Sunday a certain store sold copies of Newspaper A for

1.00 e a c han d co p i eso f N e w s p a p er B f or

1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

505-555 (Easy)

Company Q plans to make a new product next year and sell each unit of this new product at a selling price of

$2

. The variable costs per unit in each production run are estimated to be

40%

of the selling price, and the fixed costs for each production run are estimated to be

$5, 040

. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?

N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?

505-555 (Easy)

A small business invests

$9, 900

in equipment to produce a product. Each unit of the product costs

$0.65

to produce and is sold for

$1.20

. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

Sub 505 (Easy)

Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?

505-555 (Easy)

According to the table shown, the estimated number of home-schooled students in State A is approximately what percent greater than the number in State D?

Sub 505 (Easy)

On a vacation, Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent 3 4 3 4 of the euros she received. If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

505-555 (Easy)

When

n

liters of fuel were added to a tank that was already

\frac{1}{3}

full, the tank was filled to

\frac{7}{9}

of its capacity. In terms of

n

, what is the capacity of the tank, in liters?

505-555 (Easy)

For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to

505-555 (Easy)

A bicycle race on a mountain trail began at an elevation 850 meters above Town X. The race course consisted of 5 phases, with the following elevation changes: a descent of 280 meters, an ascent of 350 meters, a descent of 620 meters, an ascent of 100 meters, and a descent of 400 meters. At what elevation, in meters above or below Town X, did the race end?

Sub 505 (Easy)

Last year

48, 000 o f a cer t ain s t or e^{'} s p r o f i tw a ss ha r e d b y i t s 2 o w n er s an d t h e i r 10 e m pl oy ees . E a c h o f t h e 2 o w n er sr ece i v e d 3 t im es a s m u c ha se a c h o f t h e i r 10 e m pl oy ees . H o w m u c h d i d e a c h o w n er r ece i v e f r o m t h e

48,000 ?

505-555 (Easy)

The harvest yield from a certain apple orchard was 350 bushels of apples. If

x

of the trees in the orchard each yielded 10 bushels of apples, what fraction of the harvest yield was from these

x

trees?

Sub 505 (Easy)

A retailer purchased eggs at

2.80 p er d oz e nan d so l d t h ee g g s a t 3 e g g s f or

0.90. What was the retailer's gross profit from purchasing and selling 5 dozen eggs?

505-555 (Easy)

In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent, what is the denominator of the fraction?

555-605 (Medium)

Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

505-555 (Easy)

Jonathan, Kyle, and Michael agreed to pay equal shares of the monthly rent on an apartment. Because Jonathan has a cat, he paid a 1-time pet deposit of

$250

. The pet deposit and Jonathan's share of the monthly rent for the first month totaled

$525

. How much is the monthly rent on the apartment?

Sub 505 (Easy)

Each of the 12 squares shown is labeled x,y,v,or w. What is the ratio of the number of these squares labeled x or y to the number of these squares labeled v or w?

505-555 (Easy)

The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the month of January was

\frac{3}{2}

. If the fuel oil bill for February had been

$40

more, the corresponding ratio would have been

\frac{5}{3}

. How much was Alex's fuel oil bill for January?

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