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

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Manager
Joined: 02 Aug 2007
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If x is not equal to 0, is |x| less than 1? (1) ( x / |x|) [#permalink]

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07 Jan 2009, 23:10
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If x is not equal to 0, is |x| less than 1?

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

Kudos [?]: 74 [0], given: 0

SVP
Joined: 29 Aug 2007
Posts: 2472

Kudos [?]: 843 [0], given: 19

Re: DS |x| < 1? - MGMAT CAT [#permalink]

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07 Jan 2009, 23:17
x-ALI-x wrote:
If x is not equal to 0, is |x| less than 1?

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

1: (x/|x|) < x
if x is +ve and > 1, x/lxl = 1, which is always < x because x > 1. no.
if x is -ve fraction but > -1, x/lxl = -1, which is always < x because x is a -ve fraction > -1. yes.
so not suff..

2: |x| > x

lxl is +ve. to have lxl > x, x has to be -ve but x could be >-1 or <-1. so still not suff.

1&2: x is -ve and > -1.
so x is -ve fraction. suff.

C.
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Kudos [?]: 843 [0], given: 19

Re: DS |x| < 1? - MGMAT CAT   [#permalink] 07 Jan 2009, 23:17
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