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If x is not equal to 0, is |x| less than 1? (1) x/|x| < x

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Manager
Joined: 05 Jul 2008
Posts: 136
GMAT 2: 740 Q51 V38
If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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24 Apr 2009, 04:48
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mxb908 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x
(2) |x| > x

the OA is C

(1) x(1/|x| -1)<0 => not sufficient
(2) |x|>x => x<0 => not sufficient

C: 1/|x| -1 >0 => sufficient
Manager
Joined: 19 Aug 2006
Posts: 238

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24 Apr 2009, 08:07
mxb908 wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x
(2) |x| > x

the OA is C

I got C.

stmnt1 - clearly nsf, because x could be many values, either positive, or negative, and the expression |x|<1 could be true or false.

stmnt 2 - |x|>x => x<0
nsf

Let's combine.
because x<0 and x/|x| < x, it means that x is in the following range: -1<x<0.
Pick any number inside the -1<x<0 range, and the statement |x|<1 will always be true.
Therefore, C.
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If x is not equal to 0, is |x| less than 1? (1) x/|x| < x

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