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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]

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09 Dec 2006, 07:03
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Difficulty:

75% (hard)

Question Stats:

40% (03:07) correct 60% (01:15) wrong based on 50 sessions

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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, 13:57, edited 1 time in total.
Senior Manager
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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, 07:07

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
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Kudos [?]: 322 [0], given: 0

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, 07:12
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
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Kudos [?]: 149 [4] , given: 0

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, 07:17
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(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.
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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, 11:04
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
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Kudos [?]: 43 [1] , given: 0

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, 20:39
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Fig, you are the absolute value guru!!! Thanks!!!
_________________

Impossible is nothing

Manager
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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, 07:44
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?
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x| < x   [#permalink] 21 May 2007, 07:44
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