McGraw-Hill Education GRE 2019

If bc > 0, then b and c must have the same sign. If ac < 0, then a and c must

have different signs. Therefore, a and b must have different signs, and their

product must be negative.

Evenly Spaced Sets

An evenly spaced set is any series of numbers in which the spacing between

consecutive terms is constant. The most basic example of an evenly spaced set is

consecutive integers. In the set 1, 2, 3, 4, 5, the spacing between successive terms

is 1. Other examples are:

2, 4, 6, 8...

10, 15, 20...

3, 8 13, 18...

Note that you can describe the first example as consecutive even

integers and the second example as consecutive multiples of 5. Though

the items in the third set are not multiples of the same number, the set is

still evenly spaced since the increment between successive terms is 5.

Properties of Evenly Spaced Sets

The GRE will expect you to know certain properties of evenly spaced sets.

Property 1: All the terms in an evenly spaced set can be expressed using one of

the terms in the set.

If the sum of three consecutive multiples of 4 is 60, what is the value of the

smallest term?

SOLUTION: Approaching this algebraically, you can let a = the smallest term,

b = the middle term, and c = the largest term. Therefore, a + b + c = 60. But

notice that you have additional information about these variables! Since you

are dealing with consecutive multiples of 4, you can let b = a + 4 and c = b +

4 = a + 8. Thus using substitution, you can arrive at one equation with one

variable:

a + (a + 4) + (a + 8) = 60

3 a + 12 = 60

3 a = 48

a = 16

Property 2: The average (arithmetic mean) of an evenly spaced set = the median

of the set = the average of the endpoints.

198 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 198 12/05/17 11:51 am