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 window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

Sub 505 (Easy)

A flat patio was built alongside a house as shown in the figure above. If all angles shown are right angles, what is the area of the patio in square feet?

Sub 505 (Easy)

2018.OG.05.026.q.png [ 32.11 KiB | Viewed 51824 times ] In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

Sub 505 (Easy)

If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?

Sub 505 (Easy)

In the xy-coordinate plane, if the point (0,2) lies on the graph of the line 2x + ky = 4, what is the value of the constant k ?

505-555 (Easy)

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

555-605 (Medium)

The sum of the first hundred positive integers is divisible by?

705-805 (Hard)

In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

605-655 (Medium)

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?

605-655 (Medium)

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

705-805 (Hard)

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

505-555 (Easy)

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

705-805 (Hard)

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

705-805 (Hard)

If √ 3 − 2 x = √ 2 x + 1 3 − 2 x − − − √ = 2 x − √ + 1 , then 4 x 2 =

Sub 505 (Easy)

The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

555-605 (Medium)

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

555-605 (Medium)

Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments, how many of the parents volunteered to bring refreshments?

555-605 (Medium)

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid

3.99 f or e a c ha dd i t i o na l co m p a c t d i sc p u r c ha se d . I f a p r e f er r e d c u s t o m er p u r c ha se d a t o t a l o f 6 co m p a c t d i scs an d p ai d

15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

Sub 505 (Easy)

The sequence a 1 , a 2 , a 3 , ... , a n , ... is such that a n = a n − 1 + a n − 2 2 for all n ≥ 3 . If a 3 = 4 and a 5 = 20 , what is the value of a 6 ?

555-605 (Medium)

John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account 6 months after the account was opened?

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