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)

The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy-plane. At how many points does the graph of y = (x + 1)(x - 1)^2 + 2 intercept the x-axis?

505-555 (Easy)

Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD's vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

555-605 (Medium)

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?

505-555 (Easy)

f = 3 r (\frac{s}{1 , 000})^{2}

and if

s = 2, 000

, what is

r

in terms of

f

555-605 (Medium)

Shawana made a schedule for reading books during 4 weeks (28 days) of her summer vacation. She has checked out 12 books from the library. The number of pages in each book and the order in which she plans to read the books are shown in the table above. She will read exactly 50 pages each day. The only exception will be that she will never begin the next book on the same day that she finishes the previous one, and therefore on some days she may read fewer than 50 pages. At the end of the 28th day, how many books will Shawana have finished?

505-555 (Easy)

At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 10 months?

605-655 (Medium)

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% 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?

505-555 (Easy)

The formula

F = \frac{9}{5} C + 32

gives the relationship between the temperature in degrees Fahrenheit,

F

, and the temperature given in degrees Celsius,

C

. If the temperature is 85 degrees Fahrenheit, what is the temperature, to the nearest degree, in degrees Celsius?

705-805 (Hard)

0.99999999 1.0001 − 0.99999991 1.0003 =

505-555 (Easy)

x

and

y

are positive integers such that

y

is a multiple of 5 and

3 x + 4 y = 200

, then

x

must be a multiple of which of the following?

605-655 (Medium)

Club X has more than 10 but fewer than 40 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?

505-555 (Easy)

Which of the following expressions can be written as an integer? I.

(82 + 82)^{2}

II.

(82) (82)

III.

\frac{( 82 ) ( 82 )}{82}

505-555 (Easy)

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

505-555 (Easy)

Which of the following is equal to the average (arithmetic mean) of

(x + 2)^{2}

and

(x - 2)^{2}

505-555 (Easy)

In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?

505-555 (Easy)

x^{2} - 2 < 0

, which of the following specifies all the possible values of

x

555-605 (Medium)

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

505-555 (Easy)

Sub 505 (Easy)

(1 2 − 1 3) + (1 3 − 1 4) + (1 4 − 1 5) + (1 5 − 1 6) =

505-555 (Easy)

In Western Europe,

x

bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?

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