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)

(− 3) (− 2) =

655-705 (Hard)

If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake’s present weight, in pounds?

505-555 (Easy)

In the coordinate system above, which of the following is the equation of line l ?

655-705 (Hard)

For each student in a certain class, a teacher adjusted the student’s test score using the formula

y = 0.8 x + 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)

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?

655-705 (Hard)

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?

555-605 (Medium)

On a scale drawing, a rectangle 1 inch by 1 1 3 inches represents the floor of a room and the indicated scale is 1 inch equals 15 feet. How many square tiles 6 inches on a side will be needed to cover this floor?

655-705 (Hard)

A store reported total sales of

$385

million for February of this year. If the total sales for the same month last year was

$320

million, approximately what was the percent increase in sales?

555-605 (Medium)

Which of the following equations has 1 + √2 as one of its roots?

655-705 (Hard)

When positive integer

x

is divided by positive integer

y

, the remainder is 9. If

\frac{x}{y} = 96.12

, what is the value of

y

505-555 (Easy)

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible value of the actual area of the square region is

655-705 (Hard)

x (2 x + 1) = 0

and

(x + \frac{1}{2}) (2 x - 3) = 0

, then

x =

Sub 505 (Easy)

During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During this time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?

655-705 (Hard)

A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is

n

, then the least and greatest possible values of

n

, respectively, are

Sub 505 (Easy)

In the figure, the 6 small squares are identical, each with sides of length 1. What is the outer perimeter (shown in bold) of the entire figure?

655-705 (Hard)

For the positive numbers,

n

n + 1

n + 2

n + 4

, and

n + 8

, the mean is how much greater than the median?

605-655 (Medium)

The figure shown above consists of a shaded 9-sided polygon and 9 unshaded isosceles triangles.For each isosceles triangle,the longest side is a side of the shaded polygon and the two sides of equal length are extensions of the two adjacent sides of the shaded polygon.What is the value of a ?

655-705 (Hard)

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

555-605 (Medium)

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

655-705 (Hard)

What is the smallest integer

n

for which

2 5^{n} > 5^{12}

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