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# If x/|x|, which of the following must be true for all

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Intern
Joined: 06 Nov 2010
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If x/|x|, which of the following must be true for all [#permalink]  15 Jan 2011, 11:44
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Difficulty:

25% (low)

Question Stats:

58% (01:45) correct 41% (00:31) wrong based on 73 sessions
If \frac{x}{|x|} \lt x, which of the following must be true about x? (x \ne 0)

A. x\gt 2
B. x \in (-1,0) \cup (1,\infty)
C. |x| \lt 1
D. |x| = 1
E. |x|^2 \gt 1

M24
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 08:56, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 16817
Followers: 2771

Kudos [?]: 17573 [1] , given: 2225

Re: range of root - GMAT Club test - M24 [#permalink]  15 Jan 2011, 13:47
1
KUDOS
Expert's post
praveenvino wrote:
X/|X| < X . Which of the following must be true for all ?

a. X > 1
b. X is an element in (-1,0) U (1,inf)
c. |X| < 1
d. |X| = 1
e. |X|^2 > 1

Can some one explain how X can be zero for the above condition?

x is in the denominator so it can not equal to zero as division be zero is undefined.

Correct form of this question is below (m09 q22, discussed here: m09-q22-69937.html):

If \frac{x}{|x|} \lt x, which of the following must be true about x? (x \ne 0)
A. x\gt 2
B. x \in (-1,0) \cup (1,\infty)
C. |x| \lt 1
D. |x| = 1
E. |x|^2 \gt 1

\frac{x}{|x|}< x
Two cases:
A. x<0 --> \frac{x}{-x}<x --> -1<x. But as we consider the range x<0 then -1<x<0

B. x>0 --> \frac{x}{x}<x --> 1<x.

So the given inequality holds true in two ranges -1<x<0 and x>1.

For more check: math-absolute-value-modulus-86462.html

Hope it helps.
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Joined: 06 Nov 2010
Posts: 23
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Kudos [?]: 2 [0], given: 16

Re: range of root - GMAT Club test - M24 [#permalink]  15 Jan 2011, 14:03
Thanks Bunuel. X not equals zero condition was actually missing in the question in m24. Thanks for your help.
Re: range of root - GMAT Club test - M24   [#permalink] 15 Jan 2011, 14:03
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