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)

If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trip whose distance in miles is the whole number y?

505-555 (Easy)

The sum of the interior angles of any polygon with n sides is 180(n - 2) degrees. If the sum of the interior angles of polygon P is three times the sum of the interior angles of quadrilateral Q, how many sides does P have?

Sub 505 (Easy)

In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 19,947. Approximately what was the percent increase?

505-555 (Easy)

A computer routine was developed to generate two numbers, ( x,y), the first being a random number between 0 and 100 inclusive, and the second being less than or equal to the square root of the first. Each of the following pairs satisfies this routine EXCEPT:

505-555 (Easy)

If a, b, and c are three consecutive odd integers such that 10 < a < b < c < 20 and if b and c are prime numbers, what is the value of a + b?

605-655 (Medium)

If x ≠ 0 and x = √ 4 x y − 4 y 2 x = 4 x y − 4 y 2 − − − − √ , then in terms of y, x = ?

705-805 (Hard)

In the figure above, two searchlights S1 and S2 are located 10,000 feet apart; each covers an area of radius 10,000 feet, and each is located 8,000 feet from the railroad track. To the nearest 1,000 feet, what is the total length x of track spanned by the searchlights?

605-655 (Medium)

Of the following, which is closest to the increase from 1975 to 1980 in the amount received by the processor in producing 6 ounces of frozen orange juice?

Sub 505 (Easy)

Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for T to be in the position where S is now shown. The number of degrees through which RSTU is rotated is

555-605 (Medium)

A plane traveled k miles in its first 96 minutes of flight time. If it completed the remaining 300 miles of the trip in t minutes, what was its average speed, in miles per hour, for the entire trip?

655-705 (Hard)

A family made a down payment of

75 an d b or r o w e d t h e ba l an ceo na se t o f e n cy c l o p e d ia s t ha t cos t

400. The balance with interest was paid in 23 monthly payments of

16 e a c han d a f ina l p a y m e n t o f

9. The amount of interest paid was what percent of the amount borrowed?

605-655 (Medium)

In order to give his customers a 25 − p e r c e n t discount on the price and still net a 25 − p e r c e n t profit on the cost of an item, at what price should a merchant mark an item if it cost him $ 16.80 ?

705-805 (Hard)

If (a + b) = 4, and ab = 7/4, what is the value of a^2 – b^2?

555-605 (Medium)

In ΔPQS above, if PQ =3 and PS = 4, then PR =?

Sub 505 (Easy)

If x, y, and z are single-digit integers and 100(x) + 1,000(y) + 10(z) = N, what is the units' digit of the number N?

605-655 (Medium)

When an object is dropped, the number of feet N that it falls is given by the formula N = 1 2 g t 2 , where t is the time in seconds since it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

505-555 (Easy)

A, B, and C each drove 100-mile legs of a 300-mile course at speeds of 40, 50, and 60 miles per hour, respectively. What fraction of the total time did A drive?

555-605 (Medium)

A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds?

605-655 (Medium)

Ken left a job paying

75, 000 p er y e a r t o a cce pt a s a l es j o b p a y in g

45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?

505-555 (Easy)

If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 3. II. x is an integer multiple of 4. III. x is an integer multiple of 6.

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