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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: 25 May 2009
Posts: 141
Concentration: Finance
GMAT Date: 12-16-2011
If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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19 Jul 2009, 18:16
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If x is not equal to 0, is |x| less than 1?

(1) $$\frac{x}{|x|}< x$$

(2) $$|x| > x$$
Manager
Joined: 07 Apr 2009
Posts: 144
Re: |x| less than 1? [#permalink]

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19 Jul 2009, 19:30
IMO C

|x| > x
|x|-x > 0

x-x > 0 or -x-x > 0
not possible -2x > 0 --> x < 0 ---------------(1)

NOT SUFF x=-0.25 then |-0.25| <1 && when x = -2 then |x| > 1.

coming to the first option

$$x/|x| < x$$

$$x/x - x < 0$$ or $$x/-x -x < 0$$
1-x < 0 or -1-x <0
x > 1 or x > -1 -----------> (2)

NOT SUFF

Putting (1) & (2) together
-1 < x < 0

for sure |x| < 1
Manager
Status: Stanford GSB
Joined: 02 Jun 2008
Posts: 93
Re: |x| less than 1? [#permalink]

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20 Jul 2009, 03:17
I3igDmsu wrote:
If x is not equal to 0, is |x| less than 1?

(1) $$\frac{x}{|x|}< x$$

(2) $$|x| > x$$

Is it a valid question?

If X is not equali to O.

|x| will always have a positive value, isnt it?
Manager
Joined: 17 Apr 2009
Posts: 142
Re: |x| less than 1? [#permalink]

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20 Jul 2009, 04:01
I got A as the ans.What is the OA?
Manager
Joined: 17 Apr 2009
Posts: 142
Re: |x| less than 1? [#permalink]

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20 Jul 2009, 04:03
sandipchowdhury wrote:
I3igDmsu wrote:
If x is not equal to 0, is |x| less than 1?

(1) $$\frac{x}{|x|}< x$$

(2) $$|x| > x$$

Is it a valid question?

If X is not equali to O.

|x| will always have a positive value, isnt it?

True that |x| will always have a positive value but you have to find that is |x| less than 1?
Manager
Status: Stanford GSB
Joined: 02 Jun 2008
Posts: 93
Re: |x| less than 1? [#permalink]

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20 Jul 2009, 21:23
sorry my mistake. I was wondering how |x| can be less than 0?
Retired Moderator
Joined: 05 Jul 2006
Posts: 1741
Re: |x| less than 1? [#permalink]

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21 Jul 2009, 03:34
I3igDmsu wrote:
If x is not equal to 0, is |x| less than 1?

(1) $$\frac{x}{|x|}< x$$

(2) $$|x| > x$$

from 1

x/ /x/ < x

x</x/x
x-/x/x<0

x(1-/x/)<0
x<0 or 1-/x/<0 ie 1</x/......insuff

from 2

/x/>x ie : x is -ve.....insuff

both .........E
Re: |x| less than 1?   [#permalink] 21 Jul 2009, 03:34
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