Is x negative? 1) x^3(1-x^2) < 0 2) x^2 - 1 < 0 : DS Archive
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# Is x negative? 1) x^3(1-x^2) < 0 2) x^2 - 1 < 0

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

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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
Joined: 03 Jun 2009
Posts: 799
Location: New Delhi
WE 1: 5.5 yrs in IT
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Re: OG 11 DS #154 [#permalink]

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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]

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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, $$C$$.
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Re: OG 11 DS #154   [#permalink] 08 Jun 2009, 23:53
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# Is x negative? 1) x^3(1-x^2) < 0 2) x^2 - 1 < 0

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