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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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Joined: 23 May 2008
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Is x negative? 1) x^3(1-x^2) < 0 2) x^2 - 1 < 0 [#permalink] New post 08 Jun 2009, 22:24
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Is x negative?

1) x^3(1-x^2) < 0
2) x^2 - 1 < 0
Director
Director
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Joined: 03 Jun 2009
Posts: 805
Location: New Delhi
WE 1: 5.5 yrs in IT
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Kudos [?]: 412 [0], given: 56

Re: OG 11 DS #154 [#permalink] New post 08 Jun 2009, 23:03
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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Re: OG 11 DS #154 [#permalink] New post 08 Jun 2009, 23:53
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.
_________________

Hades

Re: OG 11 DS #154   [#permalink] 08 Jun 2009, 23:53
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