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Is x negative? 1) x^3(1-x^2) < 0 2) x^2 - 1 < 0

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Director
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Is x negative? 1) x^3(1-x^2) < 0 2) x^2 - 1 < 0 [#permalink]

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New post 08 Jun 2009, 23:24
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C
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Is x negative?

1) x^3(1-x^2) < 0
2) x^2 - 1 < 0

Kudos [?]: 82 [0], given: 0

Director
Director
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Joined: 03 Jun 2009
Posts: 785

Kudos [?]: 884 [0], given: 56

Location: New Delhi
WE 1: 5.5 yrs in IT
Re: OG 11 DS #154 [#permalink]

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New post 09 Jun 2009, 00:03
1) x^3(1-x^2) < 0: Insufficient
Let x is -ve
=> x^3 < 0 and 1-x^2 >0

for 1-x^2 >0
only possible when -1<x<1, but we don't have any info on this.

2) x^2 - 1 < 0: Insufficient
possible when -1<x<1
so, x can be both +ve or -ve

Together: Sufficient
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Manager
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Joined: 14 May 2009
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Re: OG 11 DS #154 [#permalink]

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New post 09 Jun 2009, 00:53
bigtreezl wrote:
Is x negative?

1) x^3(1-x^2) < 0
2) x^2 - 1 < 0


Question:\((x<0?)\)

(1) \(x^{3}(1-x^{2})<0\)
==> \(x^3<0\) & \(1-x^{2}>0\)
==> \(x<0\) & \((x^{2}<1 ==> -1<x<1)\)
==> \(-1<x<0\) ==> YES

or
==> \(x^3>0\) & \(1-x^{2}<0\)
==> \(x>0\) & \(x^{2}>1\)
==> \(x>0\) & \((x<-1 or x>1)\)
==> \(x>1\) ==> NO

YES&NO==> INSUFFICIENT

(2) \(x^2 - 1<0\)
==> \(x^2<1\) ==> \(-1<x<1\) ==> YES/NO, INSUFFICIENT

(1&2) Rearrange \(x^2 - 1<0\)
to \(-(1-x^2)<0\)
then to \(1-x^2>0\)

So \(1-x^2\) is +
sub into equation 1
(1) \(x^{3}+<0\)
\(x^3<0\)
==> x<0

SUFFICIENT

Final Answer, \(C\).
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Re: OG 11 DS #154   [#permalink] 09 Jun 2009, 00:53
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