McGraw-Hill Education GRE 2019

Addition and Subtraction

Property 1: In addition or subtraction, the result will be even if the numbers being

added or subtracted are the same (both odd or both even), and the result will be

odd if the numbers being added or subtracted are different (one odd and one even).

PROPERTY EXAMPLE

odd +/– odd = even 3 + 5 = 8

even +/– even = even 4 + 10 = 14

even +/– odd = odd 8 – 3 = 5

odd +/– even = odd 5 + 8 = 13

Multiplication

Property 2: For a product to be even, at least one of the factors must be even.

PROPERTY EXAMPLE

even × even = even 4 × 6 = 24

even × odd = even 6 × 5 = 30

odd × even = even 3 × 8 = 24

odd × odd = odd 7 × 5 = 35

even ×... = even 4 × 5 × 7 × 11 = 1,540

(even)x = even^43 = 64

(odd)x = odd 33 = 27

Let’s look at a sample question that tests these properties:

For this question, indicate all of the answer choices that apply.

If x and y are integers and 3x + 2y is even, then which of the following must

be true?

A x is even

B x is odd

C xy is even

D x + y is even

E x^2 is odd

SOLUTION: Use properties of odds and evens to deduce what must be true

about the variables.

3 x + 2y = even

CHAPTER 9 ■ NUMBER PROPERTIES 185

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