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# Is |x| < 1 ?

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Senior Manager
Joined: 10 Apr 2012
Posts: 278

Kudos [?]: 1217 [0], given: 325

Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Is |x| < 1 ? [#permalink]

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13 Feb 2013, 04:55
1
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Difficulty:

45% (medium)

Question Stats:

65% (01:04) correct 35% (01:20) wrong based on 62 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, 09:16, edited 2 times in total.
Edited the question.

Kudos [?]: 1217 [0], given: 325

Senior Manager
Joined: 24 Aug 2009
Posts: 493

Kudos [?]: 878 [2], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Is |x|<1 [#permalink]

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13 Feb 2013, 05:13
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, 09:15, edited 2 times in total.

Kudos [?]: 878 [2], given: 276

Senior Manager
Joined: 10 Apr 2012
Posts: 278

Kudos [?]: 1217 [2], given: 325

Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Re: Is |x|<1 [#permalink]

### Show Tags

13 Feb 2013, 06:37
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| )

Kudos [?]: 1217 [2], given: 325

Board of Directors
Joined: 01 Sep 2010
Posts: 3422

Kudos [?]: 9491 [0], given: 1203

Re: Is |x|<1 [#permalink]

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13 Feb 2013, 07:02
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 .............
_________________

Kudos [?]: 9491 [0], given: 1203

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

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