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
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