Hi All,

This question is loaded with Number Property rules. If you know the rules, then you can make relatively quick work of this question; you can also solve it by TESTing VALUES...

We're told that X ≠ 0. We're asked if (X^2) /(|X|) < 1. This is a YES/NO question.

Before dealing with the two Facts, I want to point out a couple of Number Properties in the question stem:

1) X^2 will either be 0 or positive.

2) |X| will either be 0 or positive.

3) For the fraction in the question to be LESS than 1, X^2 must be LESS than |X|.

Fact 1: X < 1

IF...

X = 1/2

(1/4)/|1/2| = 1/2 and the answer to the question is YES

IF...

X = -1

(1)/|-1| = 1 and the answer to the question is NO

Fact 1 is INSUFFICIENT

Fact 2: X > −1

IF...

X = 1/2

(1/4)/|1/2| = 1/2 and the answer to the question is YES

IF...

X = 1

(1)/|1| = 1 and the answer to the question is NO

Fact 2 is INSUFFICIENT

Combined, we know...

-1 < X < 1

Since X cannot equal 0, X must be a FRACTION (either negative or positive). In ALL cases, X^2 will be LESS than |X|, so the fraction will ALWAYS be less than 1 and the answer to the question is ALWAYS YES.

Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,

Rich

_________________

# Rich Cohen

Co-Founder & GMAT Assassin

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