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# Is |x| < 1 ?

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Senior Manager
Joined: 10 Apr 2012
Posts: 276
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
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Kudos [?]: 511 [0], given: 325

Is |x| < 1 ? [#permalink]

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13 Feb 2013, 05:55
1
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Difficulty:

45% (medium)

Question Stats:

66% (02:06) correct 34% (01:17) wrong based on 46 sessions

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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, 10:16, edited 2 times in total.
Edited the question.
Director
Joined: 24 Aug 2009
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Schools: Harvard, Columbia, Stern, Booth, LSB,
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13 Feb 2013, 06:13
2
KUDOS
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?

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, 10:15, edited 2 times in total.
Senior Manager
Joined: 10 Apr 2012
Posts: 276
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 3

Kudos [?]: 511 [2] , given: 325

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13 Feb 2013, 07:37
2
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| )

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13 Feb 2013, 08:02
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

I agree with you .............
_________________
Re: Is |x|<1   [#permalink] 13 Feb 2013, 08:02
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