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

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Manager
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X/ |X| < X. Which of the following must be true about X? [#permalink] New post 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??
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Manager
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 [#permalink] New post 09 Sep 2005, 21:21
x/lxl < x => x<xlxl
if x>0
lxl>1 => x>1 or x<-1, combined with x>0: x>1
if x<0
lxl<1 => -1<x<1, combined with x<0: -1<x<0

Only X>-1 satisfies both possibilities. but not x>1 which violets the second one.
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 [#permalink] New post 10 Sep 2005, 05:40
Excluding the case X=0,

X / |X| = sign(X)

So X / |X| = 1 if X>0, and = -1 if X<0

So if X<= -1 then X / |X| = -1 >= X

So if X / |X| < X then X > -1
Manager
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Thanks! [#permalink] New post 10 Sep 2005, 14:18
You guys rock on multiple levelts...

Cheers,
Thanks!   [#permalink] 10 Sep 2005, 14:18
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