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)

From the consecutive integers -10 to 10 inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?

605-655 (Medium)

The graph shows the number of computers assembled during each of 6 consecutive days. From what day to the next day was the percent change in the number of computers assembled the greatest in magnitude?

555-605 (Medium)

For each student in a certain class, a teacher adjusted the student’s test score using the formula y = 0.8x + 20, where x is the student’s original test score and y is the student’s adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?

605-655 (Medium)

n = 20! + 17

, then

n

is divisible by which of the following? I. 15 II. 17 III. 19

555-605 (Medium)

Five batches of 100 nails each are taken from a production line. The numbers of defective nails in the first four batches are 2, 4, 3, and 5, respectively. If the fifth batch has either 1, 2, or 6 defective nails, for which of these values does the average (arithmetic mean) number of defective nails per batch for the five batches equal the median number of defective nails for the five batches?

605-655 (Medium)

Exchange Rates in a Particular Year

$1 = 5.3

francs

$1 = 1.6

marks An American dealer bought a table in Germany for 480 marks and sold the same table in France for 2,385 francs. What was the dealer’s gross profit on the two transactions in dollars?

555-605 (Medium)

A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

605-655 (Medium)

The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?

List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E - S ?

605-655 (Medium)

According to a certain estimate, the depth

N (t)

, in centimeters, of the water in a certain tank at

t

hours past 2:00 in the morning is given by

N (t) = - 20 (t - 5)^{2} + 500

for

0 \leq t \leq 10

. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?

Sub 505 (Easy)

If p, q, r, and s are as shown on the number line above, which of the following products is greatest?

605-655 (Medium)

After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

555-605 (Medium)

The table above is a 3 by 3 grid of 9 numbers, 5 of which are given. The 4 numbers that are not given are denoted by A, B, C, and D. The product of the numbers in each row and in each column is the same for all rows and columns. What is the value of the product ABCD ?

605-655 (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)

The sum of all the integers k such that −26 < k < 24 is

605-655 (Medium)

M

is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?

Sub 505 (Easy)

Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

605-655 (Medium)

Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in

x

hours. Working alone at its constant rate, Machine A produces 800 nails in

y

hours. In terms of

x

and

y

, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?

505-555 (Easy)

Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

605-655 (Medium)

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?

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