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Is |x| < 1 ?

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Is |x| < 1 ? [#permalink] New post 13 Feb 2013, 04:55
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Question Stats:

68% (02:06) correct 32% (00:49) wrong based on 31 sessions
Is |x| < 1 ?

(1) x^4 -1 > 0

(2) 1/ (1-|x|) > 0

Could any one tell me the approach without testing the numbers ?

thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Feb 2013, 09:16, edited 2 times in total.
Edited the question.
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Re: Is |x|<1 [#permalink] New post 13 Feb 2013, 05:13
2
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Is |x|<1
1)X^4 -1 >0
2) 1/ 1-|x| >0

Question stem asks whether Is -1<x<1
Statement 1-X^4 -1 >0 ------>X^4 >1----> In order for this to be true x must be either greater than 1 or less than -1 i.e. x>1 or x<-1
In other words x does not fall in the range -1 to 1
Thus Sufficient

Statement 2 - 1/ 1-|x| >0
LHS is greater than 0 i.e. (any Positive number). Becuase the Numerator is positive Denominator has to be positive as well
Denominator = 1- |x|
In order to keep the Denominator positive, the Absolute value of x < Absolute value of 1
i.e. x range between -1 to 1.
Thus sufficient.

I hope this explanation helps.
By the way, this is a very POOR quality question as both options give two different answers.

Fame

guerrero25 wrote:
Thanks for the explanation , Can we not have consistent answers to conclude that 1 & 2 independently are true?
Please clarify ..

Hi Guerrero,

That's possible logically but GMAT does not consider the same PRUDENT as you can observe that none of OG questions has two different answers.

Fame
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Last edited by fameatop on 13 Feb 2013, 09:15, edited 2 times in total.
2 KUDOS received
Senior Manager
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Joined: 10 Apr 2012
Posts: 274
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 2

Kudos [?]: 98 [2] , given: 322

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Re: Is |x|<1 [#permalink] New post 13 Feb 2013, 06:37
2
This post received
KUDOS
fameatop wrote:
Is |x|<1
1)X^4 -1 >0
2) 1/ 1-|x| >0

Question stem asks whether Is -1<x<1
Statement 1-X^4 -1 >0 ------>X^4 >1----> In order for this to be true x must be either greater than 1 or less than -1 i.e. x>1 or x<-1
In other words x does not fall in the range -1 to 1
Thus Sufficient

Statement 2 - 1/ 1-|x| >0
LHS is greater than 0 i.e. (any Positive number). Becuase the Numerator is positive Denominator has to be positive as well
Denominator = 1- |x|
In order to keep the Denominator positive, the Absolute value of x < Absolute value of 1
i.e. x range between -1 to 1.
Thus sufficient.

I hope this explanation helps.
By the way, this is a very POOR quality question as both options give two different answers.

Fame


Thanks for the explanation , Can we not have consistent answers to conclude that 1 & 2 independently are true?

1) False for all the conditions ( taking |2| & |-2| both satisfy the condition )


2) True for all the conditions ( Taking |-1/2| & |-1/2| )

Please clarify ..
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Re: Is |x|<1 [#permalink] New post 13 Feb 2013, 07:02
Expert's post
fameatop wrote:
Is |x|<1
1)X^4 -1 >0
2) 1/ 1-|x| >0

Question stem asks whether Is -1<x<1
Statement 1-X^4 -1 >0 ------>X^4 >1----> In order for this to be true x must be either greater than 1 or less than -1 i.e. x>1 or x<-1
In other words x does not fall in the range -1 to 1
Thus Sufficient

Statement 2 - 1/ 1-|x| >0
LHS is greater than 0 i.e. (any Positive number). Becuase the Numerator is positive Denominator has to be positive as well
Denominator = 1- |x|
In order to keep the Denominator positive, the Absolute value of x < Absolute value of 1
i.e. x range between -1 to 1.
Thus sufficient.

I hope this explanation helps.
By the way, this is a very POOR quality question as both options give two different answers.

Fame



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Re: Is |x|<1   [#permalink] 13 Feb 2013, 07:02
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