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

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Senior Manager
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK
If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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09 Dec 2006, 08:03
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If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x

[Reveal] Spoiler: OA

_________________

Impossible is nothing

Last edited by Harley1980 on 07 Jun 2015, 14:57, edited 1 time in total.
Senior Manager
Joined: 23 Jun 2006
Posts: 387
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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09 Dec 2006, 08:07

x is not 0 so:
x/|x|<x => 1/|x|<1 => |x| > 1 sufficient to give negative answer to question.

st 2 is not sufficient. consider x=-2 x=-0.5 both satisfy st2 but give different answers to question.

hence A.
Senior Manager
Joined: 23 Jun 2006
Posts: 387
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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09 Dec 2006, 08:12
my first wrong answer here in the forum!!!

ok i missed it.

it is C.

you must deduce from st2 that x is negative.
and then do the right math to deduce the right answer...

good i gave it a second thought.

SVP
Joined: 01 May 2006
Posts: 1796
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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09 Dec 2006, 08:17
4
KUDOS
(C) for me

From 1:
x/|x| < x
<=> x/|x| - x < 0
<=> x*(1/|x| - 1) < 0
<=> x*(1 - |x|) < 0 as |x| is always positive and here cannot be zero

implies that:
x < 0 and 1 - |x| > 0
or
x > 0 and 1 - |x| < 0

So we have:
- 1 < x < 0
or
x > 1

INSUFF.

From 2:
|x| > x implies that x < 0 but we cannot know x < -1 or x > -1 or x = -1

INSUFF.

Both statments
From 2, x is negative. From 1, we can imply that the only remaning, negative domain is -1 < x < 0.
Hence, |x| < 1.

SUFF.
Senior Manager
Joined: 20 Feb 2006
Posts: 373
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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09 Dec 2006, 12:04
I picked numbers:

From 1)
a) If x =2 2/2 = 1 So 1 is less than x
b) If x = -2 -2/2 = -1 So 1 is greater than x
c) If x = 1/2 (1/2)/(1/2) = 2 So 2 is greater than 1/2
d) If x = -1/2 (-1/2)/(1/2) = -2 So -2 is less than -1/2

a and d satisfy x/lxl<x but we still cant answer stem
INSUFF

From 2)
This just tells us that x is negative
From b) and d) above, you can see that b) doesn't satisfy stem but d) does so INSUFF

Taking both together we know that x is negative and -1<x<0 so SUFF

Senior Manager
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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09 Dec 2006, 21:39
1
KUDOS
Fig, you are the absolute value guru!!! Thanks!!!
_________________

Impossible is nothing

Manager
Joined: 09 Nov 2006
Posts: 128
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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21 May 2007, 08:44
The question asks whether -1<X<1>1 and (2) gives us that X is negative, how can we conclude that both statements together are sufficient?

I think it is E?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16509
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x [#permalink]

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26 Jun 2017, 08:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x   [#permalink] 26 Jun 2017, 08:25
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