GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

If all the points were graphed for -2 :::;; x:::;; 2, then the graph would appear as follows.

y

3

2

1

-2

1 2 X

The graph of a quadratic function is called a parabola and always has the shape of the curve above,

although it may be upside down or have a greater or lesser width. Note that the roots of the equation

f(x) = x2 -l = 0 are x = l and x = -l; these coincide with the x-·intercepts since x-intercepts are

found by setting y = 0 and solving for x. Also, they-intercept isf(0) = -1 because this is the value of y

corresponding to x = 0. For any function f the x-intercepts are 1the solutions of the equation J(x) = 0

and they-intercept is the value f(O).

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,

Rate x Time = Distance.

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 rate X time = distance, simply multiply 70 km/hour x 4 hours. 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^200 = 5 hours to travel the first 200 miles.

40