GMAT Quantitative Review

3.0 Math Review

3.4 Word Problems

Many of the principles discussed in this chapter are used to solve word problems. The following discussion of word problems illustrates some of the techniques and concepts used in solving such problems.

1. Rate Problems

The distance that an object travels is equal to the product of the average speed at which it travels and the amount of time it takes to travel that distance, that is,

.

Example 1: If a car travels at an average speed of 70 kilometers per hour for 4 hours, how many kilometers does it travel?

Solution: Since , simply multiply . Thus, the car travels 280 kilometers in 4 hours.

To determine the average rate at which an object travels, divide the total distance traveled by the total amount of traveling time.

Example 2: On a 400-mile trip, Car X traveled half the distance at 40 miles per hour (mph) and the other half at 50 mph. What was the average speed of Car X?

Solution: First it is necessary to determine the amount of traveling time. During the first 200 miles, the car traveled at 40 mph; therefore, it took hours to travel the first 200 miles.

During the second 200 miles, the car traveled at 50 mph; therefore, it took hours to travel the second 200 miles. Thus, the average speed of Car X was mph. Note that the average speed is not .

Some rate problems can be solved by using ratios.

Example 3: If 5 shirts cost $44, then, at this rate, what is the cost of 8 shirts?

Solution: If c is the cost of the 8 shirts, then . Cross multiplication results in the equation

The 8 shirts cost $70.40.