McGraw-Hill Education GRE 2019

Many test-takers mistakenly assume that since a^4 > 0, a must be greater than zero.

However, remember that even exponents hide the sign of the base. Whether the

base is positive or negative, the result of a variable raised to an even exponent will

always be positive. Thus F is not necessarily true.

Quantitative Comparison Strategy: Positives and Negatives

The GRE loves testing properties of positives and negatives in Quantitative

Comparison questions. One important building block of success for the savvy test-

taker is to identify situations in which these properties are being tested.

Situation 1 You are told that an unknown is greater than or less than zero.

If the stem says that x > 0, then you know that x is positive. If it says that xy < 0,

then you know that xy is negative. Once you recognize that these properties are

being tested, you can then start using the rules that have been covered.

Situation 2 One of the quantities has a value of zero.

If you are comparing an unknown to zero, your ultimate goal is to determine the

sign of that unknown. Remember that you can determine its sign without knowing

its actual value.

x ≠ 0

QUANTITY A QUANTITY B

x^16 + 1 0 A B C D

SOLUTION: Since you are comparing (x^16 + 1) to zero, you should focus on

determining the sign of Quantity A. Since the exponent on x^16 is even, x^16 > 0.

Thus x^16 + 1 > 0. The correct answer is Quantity A.

Situation 3 One of the quantities has an even exponent,

and the other quantity has an odd exponent.

Since the result of an even exponent hides the sign of the base, and the result of an

odd exponent preserves the sign of the base, these properties are fertile ground to

test your knowledge of positives and negatives.

q is an integer

QUANTITY A QUANTITY B

(– 4,012)^2 q (– 4,012)^2 q + 1 A B C D

SOLUTION: In both quantities, the base is negative. Since the exponent in

Quantity A is even, the value in Quantity A must be positive. Since the

exponent in Quantity B is odd, the value in Quantity B must be negative. The

correct answer is A.

CHAPTER 9 ■ NUMBER PROPERTIES 191

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