GRE Sample Math-Test Questions: Word Problems
In addition to number-crunching on the GRE, you also need to be able to translate word problems into math so you can solve them. The GRE uses common types of word problems, each of which you solve using one or more standard strategies.
Bill is budgeting the expenditure of a new car based on his gross income from last year. If his gross income from last year was $50,000 and Bill wants to spend between 15% and 30% on a new car, which of the following could be the cost of the new car?
Indicate all possible costs of the new car.
A furniture dealer sold two sofas for $400 each, for a 25% profit on one and a 20% loss on the other.
Which of the following statements is true about the two quantities?
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
A car travels at a constant rate of 20 meters per second. How many kilometers does it travel in 10 minutes? (1 kilometer = 1,000 meters)
A circular pool of radius r feet is surrounded by a circular sidewalk of width r/2 feet. In terms of r, what is the area of the sidewalk?
Answers and explanations
A, B, C, and D.
These four answer choices are correct because 15 to 30 percent of $50,000 is $7,500 to $15,000. In this type of question, you select all correct answer choices.
The percents profit and loss are based on the dealer’s purchase price, not the dealer’s selling price. If he sold a sofa for $400 at a 25 percent profit, then he sold it for 125 percent, or 5/4, of what he paid for it, which is x, so
The net gain was $400 – $320 = $80.
The dealer sold the other sofa for $400 at a 20 percent loss, or for
of what he paid for it (call it y). Therefore, the dealer purchased it for
The net loss was $500 – $400 = $100, so Quantity B is larger. If you chose Choice (A), then you calculated the profit and loss on the dealer’s sale prices of $400, not the dealer’s purchase prices.
Set up the conversions as fractions and do the math:
Note that the three zeros in the numerators cancel the three zeros in the denominator of the second fraction.
If the radius of the pool is r, then the radius from the center of the pool to the outer circumference of the sidewalk is
First, calculate the area of the pool and sidewalk by substituting
for r in the equation for the area of a circle:
Next, calculate the area of the pool alone, which is easy:
Finally, subtract the area of the pool from the total area of the pool plus the sidewalk, remembering that you need a common denominator to subtract: