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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605-655 (Medium)

November 16, 2001, was a Friday. If each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was November 16, 2014 ?

Sub 505 (Easy)

The graph of the equation xy = k, where k < 0, lies in which two of the quadrants shown above?

655-705 (Hard)

In the figure above, ABCD is a parallelogram and E is the midpoint of side AD. The area of triangular region ABE is what fraction of the area of the quadrilateral region BCDE?

Sub 505 (Easy)

In triangle ABC above, what is x in terms of z ?

Sub 505 (Easy)

In the xy plane, the distance between the origin and the point (4,5) is the same as the distance between which of the following two points?

505-555 (Easy)

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?

Sub 505 (Easy)

The price of a coat in a certain store is

500. I f t h e p r i ceo f t h eco a t i s t o b er e d u ce d b y

150, by what percent is the price to be reduced?

555-605 (Medium)

One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K ?

Sub 505 (Easy)

Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?

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?

Sub 505 (Easy)

The table shows a summary of the ticket sales from four performances of a certain play. What is the difference between the maximum and the minimum ticket-sale revenue from a single performance?

Sub 505 (Easy)

The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median number of cars sold per day for the seven days?

555-605 (Medium)

If m and p are positive integers and m 2 + p 2 < 100 , what is the greatest possible value of mp ?

705-805 (Hard)

How many of the integers that satisfy the inequality (x + 2) (x + 3) (x − 2) ≥ 0 are less than 5?

605-655 (Medium)

The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room. Thus, after someone enters or exits the room, the light remains on for only 15 minutes unless the door opens again and reset the timer for another 15 minutes. If the times listed above are the times at which the door opened from 8:00 to 10:00, approximately how many minutes during this two-hour period was the light off ?

555-605 (Medium)

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

Sub 505 (Easy)

What number is 108 more than two-thirds of itself?

555-605 (Medium)

The price of gasoline at a service station increased from

1.65 p er g a l l o n l a s tw ee k t o

1.82 per gallon this week. Sally paid $26.40 for gasoline last week at the station. How much more will Sally pay this week at the station for the same amount of gasoline?

555-605 (Medium)

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers?

Sub 505 (Easy)

In quadrilateral ABCD above, what is the length of AB ?

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