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

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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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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.
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Re: range of root - GMAT Club test - M24 [#permalink]  15 Jan 2011, 13:47
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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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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.
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Re: If x/|x|, which of the following must be true for all [#permalink]  03 Nov 2014, 10:55
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Re: If x/|x|, which of the following must be true for all [#permalink]  11 Dec 2014, 23:00
A must be true too.
If x>1 satisfy x/|x|<x
then x>2 will do too.
can anyone explain choice A? thanks!
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Re: If x/|x|, which of the following must be true for all [#permalink]  12 Dec 2014, 05:51
Expert's post
pinguuu wrote:
A must be true too.
If x>1 satisfy x/|x|<x
then x>2 will do too.
can anyone explain choice A? thanks!

x > 2 is NOT necessarily true. Consider x = -1/2.
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Re: If x/|x|, which of the following must be true for all   [#permalink] 12 Dec 2014, 05:51
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