McGraw-Hill Education GRE 2019

Multiplication and Division

When multiplying or dividing two terms, the result will be positive if the terms

are the same sign (both positive or both negative) and negative if the two terms are

different signs (one positive and one negative).

+ × + = + + ÷ + = +

− × − = + − ÷ − = +

− × + = − − ÷ + = −

+ × − = − + ÷ − = −

If y – x^1 < 0, then which of the following must be true?

A y > 0

B x > 0

C xy > 0

D y > x

E x > y

SOLUTION: If y – x^1 is negative, then the numerator and denominator must

have different signs. Since the numerator is positive, y – x must be negative.

Algebraically y – x < 0. Add x to both sides: y < x. Of the choices, the only

one matching what you have deduced is E.

Many positive/negative questions will raise the terms to an exponent.

For such questions, it’s important to remember a property that is

covered in Chapter 11 on quadratics: When a variable is raised to an even

exponent, the result will always be positive. When a variable is raised to an

odd exponent, the sign of the result will always be the same as the sign of

the base.

If a^4 b^3 c^7 > 0, then which of the following must be true? (Indicate all the apply.)

A a > 0

B b > 0

C bc > 0

D b/c > 0

E ab > 0

F abc > 0

SOLUTION: You are not told the sign of any of the unknowns, but since a is

raised to an even exponent, you know that a^2 is positive. Thus you have:

(+) × (b^3 ) × (c^7 ) > 0. Since + × + = +, it must be true that b^3 × c^7 is positive.

Since b and c are each raised to odd exponents, the signs of b^3 and c^7 will be

the same as the signs of b and c, respectively. Thus you know that bc > 0.

If bc > 0, then b and c must have the same sign, meaning that their product

and their quotient are positive. The correct answer is C and D.

190 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 190 12/05/17 11:51 am