McGraw-Hill Education GRE 2019

Choice E: If x is 2, then x^2 = 4. 4 is a multiple of 4. If x is 8, then x^2 = 64. 64

is a multiple of 4. Both cases lead to the conclusion that x^2 is a multiple of 4.

→ E is true.

5. B, D, and E For a product to be odd, all factors must be odd. Thus x and
   (y + 3) must be odd. If y + 3 is odd, then y is even. Now evaluate the choices:
   Choice A: As previously shown, x is odd. → A is not true.
   Choice B: As previously shown, y is even. → B is true.
   Choice C: For a product to be odd, all factors must be odd. As previously
   shown, y is even. Thus xy is even. → C is not true.
   Choice D: See the explanation for C. → D is true
   Choice E: See the explanation for A. → E is true
   Choice F: See the explanation for B. → F is not true


6. A, C, D, and E Since a + b is an even integer, a and b must both be odd
   or both be even. Since bc is an odd integer, b and c must both be odd.
   If a + b = even and b = odd, then a = odd. Thus a, b, and c are all odd.
   Evaluate the choices:
   Choice A: odd + odd = even → A is true.
   Choice B: odd × odd = odd → B is not true.
   Choice C: odd × odd = odd → C is true.
   Choice D: odd – odd = even → D is true.
   Choice E: odd × odd × odd = odd → E is true.

Positives and Negatives

All About Zero

A number’s position in relation to zero determines its sign. If a number is greater

than zero, then it is positive. If a number is less than zero, it is negative.

Number line

0

Negative Positive

Generally, when you are told or asked whether a term is greater than zero or less

than zero, you should interpret it using properties of positives and negatives. For

example, if you are told that xy > 0, think of this information as “xy is positive,”

and proceed to use the rules covered in this chapter. As with odds and evens, you

will need to know certain properties of positive and negative numbers.

CHAPTER 9 ■ NUMBER PROPERTIES 189

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