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X/ |X| < X. Which of the following must be true about X? [#permalink]
09 Sep 2005, 19:40

X/ |X| < X. Which of the following must be true about X?

A) X > 1
B) X > -1
C) |X| < 1
D) |X| = 1
E) |X|^2 > 1

Explanation

If X > 0, the inequality turns into X > 1. If X < 0, the inequality turns into X > -1. In each of the cases X > -1, therefore X > -1 is true for all possible X. Counter-examples to show that other choices are not necessarily true:
(A),(D),(E) X = -1/2;
(C) X = 5.

The OA is B but I'm having a little trouble understanding why it is not A. For example, if X>-1 then X could = 1 and 1/1 is NOT < 1...But if A is the case and X > 1 it seems to work....Can any help a gmat brother out??