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# x/|x| < x. Which must be true? x > 1 x> -1 |x| <

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CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 349 [0], given: 4

x/|x| < x. Which must be true? x > 1 x> -1 |x| < [#permalink]  17 Dec 2007, 08:15
x/|x| < x. Which must be true?

x > 1
x> -1
|x| < 1
|X| = 1
|x|^2 > 1
Manager
Joined: 20 Jun 2007
Posts: 157
Followers: 1

Kudos [?]: 16 [0], given: 0

Can't think of a clever way to do this, but it's quick to try a few numbers:

1/2 : 1 < 1/2 not true
1: 1 < 1 not true
2: 1 < 2 true
-1: -1 < -1 not true
-2 -1 <2>-1, B.
SVP
Joined: 29 Aug 2007
Posts: 2497
Followers: 57

Kudos [?]: 556 [0], given: 19

Re: X/|x| < X [#permalink]  17 Dec 2007, 09:23
bmwhype2 wrote:
x/|x| < x. Which must be true?

x > 1
x> -1
|x| < 1
|X| = 1
|x|^2 > 1

A. x / |x| < x only when x>1 because x/lxl can be either -1, 1, or infinitive but infinitive doesnot solve the problem. so only if x >1, x > x/lxl. if x >-1, x is not greater than x/lxl if x is a +ve fraction.

therefore, x > 1. So A.
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 99 [0], given: 0

Here, other explanations : http://www.gmatclub.com/forum/t54918
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 349 [0], given: 4

how do i search for "X / |X| < x"
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 99 [0], given: 0

bmwhype2 wrote:
how do i search for "X / |X| < x"

Indeed, it's not possible
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