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

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If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]  02 Nov 2009, 04:16
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Question Stats:

57% (02:24) correct 43% (01:37) wrong based on 74 sessions
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2013, 02:34, edited 1 time in total.
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Re: MGMAT inequality [#permalink]  02 Nov 2009, 05:34
gmatforce wrote:
If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x

B

(1)
x=-1/2
-1<-1/2

x=2
1<2
Can't say if x is less than 1

(2)
x has to be negative for the absolute value to be greater. Sufficient.
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Re: MGMAT inequality [#permalink]  02 Nov 2009, 06:25
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Expert's post
I think B is not correct. This question was discussed before, below see my post from the earlier discussion:

x#0, is $$|x|<1$$? Which means is $$-1<x<1$$? (x#0)

(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$

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

Two ranges $$-1<x<0$$ or $$x>1$$. Which says that x either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)

(2) $$|x| > x$$ Well this basically tells that $$x$$ is negative. But still if we want to see how it works:
Two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.

$$x>0$$ --> $$x>x$$: never correct.

Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)

(1)+(2) $$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$. Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.

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Re: MGMAT inequality [#permalink]  02 Nov 2009, 06:34
Bunuel wrote:
I think B is not correct. This question was discussed before, below see my post from the earlier discussion:

x#0, is $$|x|<1$$? Which means is $$-1<x<1$$? (x#0)

(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$

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

Two ranges $$-1<x<0$$ or $$x>1$$. Which says that x either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)

(2) $$|x| > x$$ Well this basically tells that $$x$$ is negative. But still if we want to see how it works:
Two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.

$$x>0$$ --> $$x>x$$: never correct.

Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)

(1)+(2) $$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$. Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.

Oh grossly misread the Q as x<1. Thanks for the correction!
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Re: MGMAT inequality [#permalink]  03 Nov 2009, 20:18
Bunuel, Gmat community's happy to got you.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]  16 Jan 2013, 23:40
1
KUDOS
gmatforce wrote:
If x is not equal to 0, is |x| less than 1?
(1) x/|x| < x
(2) |x| > x

This is my most feared question type because it requires you to try out values but practice truly reduces that anxiety...

1.
Test x=2: 1 < 2 (This works for the equation but |x| is not less than 1) NO!
Test x=-1/4: -1 < -1/4 (This works for the equation and |x| is less than 1) YES!
INSUFFICIENT.

2. |x| > x
This means x is negative value.
x = -1: |x| is not less than 1 NO!
x = -1/4: |x| is less than 1 YES!
INSUFFICIENT!

Together: We only test (-) values with x/|x| < x
x=-1: No!
x=-1/4: Yes!

So the only valid solution for x/|x| < x that is negative is a fraction.
Fractions are |x| less than 1. YES!

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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]  05 Feb 2014, 12:55
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x   [#permalink] 05 Feb 2014, 12:55
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