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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505-555 (Easy)

A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 45 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?

555-605 (Medium)

An author received

0.80 in r oy a l t i es f or e a c h o f t h e f i r s t 100, 000 co p i eso f h er b oo k so l d, an d

0.60 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?

Sub 505 (Easy)

Today, Anna is 10 years older than Michelle. If fifteen years ago, Anna was twice as old as Michelle, how old is Michelle today?

505-555 (Easy)

If x = (0.08) 2 , y = 1 (0.08) 2 and z = (1 − 0.08) 2 − 1 , which of the following is true?

505-555 (Easy)

Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?

Sub 505 (Easy)

On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

Sub 505 (Easy)

Of the 65 cars on a car lot, 45 have air-conditioning, 30 have power windows, and 12 have both air-conditioning and power windows. How many of the cars on the lot have neither air-conditioning nor power windows?

Sub 505 (Easy)

For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S = 60 k d 2 , where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

555-605 (Medium)

Dick and Jane each saved

3, 000 in 1989. I n 1990 D i c k s a v e d 8 p er ce n t m or e t hanin 1989, an d t o g e t h er h e an dJ an es a v e d a t o t a l o f

5,000. Approximately what percent less did Jane save in 1990 than in 1989?

655-705 (Hard)

A factory that employs 1,000 assembly-line workers pays each of these workers $6 per hour for the first 35 hours worked during a week and 1.25 times that rate for hours worked in excess of 35. What was the total payroll for the assembly line workers for a week in which 60 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 50 hours?

Sub 505 (Easy)

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

Sub 505 (Easy)

Reggie purchased a car costing

8, 700. A s a d o w n p a y m e n t h e u se d a

2,300 insurance settlement and an amount from his savings equal to 15 percent of the difference between the cost of the car and the insurance settlement. If he borrowed the rest of the money needed to purchase the car, how much did he borrow?

555-605 (Medium)

In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?

Sub 505 (Easy)

The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?

Sub 505 (Easy)

What is 45 percent of 7 12 7 12 of 240 ?

555-605 (Medium)

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

Sub 505 (Easy)

During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?

605-655 (Medium)

Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?

505-555 (Easy)

An optometrist charges

150 p er p ai r f or so f t co n t a c tl e n ses an d

85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold?

Sub 505 (Easy)

If d = 2.0453 and d* is the decimal obtained by rounding d to the nearest hundredth, what is the value of d* - d ?

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