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# Data sufficiency (OG) Is x negative? 1) x^3(1-x^2)<0 2)

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Intern
Joined: 23 May 2008
Posts: 48
Data sufficiency (OG) Is x negative? 1) x^3(1-x^2)<0 2) [#permalink]

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08 Oct 2008, 10:49
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Data sufficiency (OG)

Is x negative?

1) x^3(1-x^2)<0
2) x^2-1<0
Senior Manager
Joined: 04 Jan 2006
Posts: 276
Re: Algebra Arithmetic Operations + Inequalities [#permalink]

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08 Oct 2008, 11:23
snowbirdskier wrote:
Data sufficiency (OG)

Is x negative?

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

1) x^3(1-x^2) < 0
-x^3(x^2-1) < 0
x^3(x^2-1) > 0
x^3(x-1)(x+1) > 0
x = (-1,0) U (1, oo)
Insufficient.

2) x^2-1 <0
(x-1)(x+1) < 0
x = (-1,1)
Insufficient.

1) & 2)
x^3(x^2-1) > 0
Since (x^2-1) is a negative number
x^3 * [negative number] > 0
x^3 must be a negative number also.
Therefore, x < 0.

Senior Manager
Joined: 04 Jan 2006
Posts: 276
Re: Algebra Arithmetic Operations + Inequalities [#permalink]

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08 Oct 2008, 11:24
snowbirdskier wrote:
Data sufficiency (OG)

Is x negative?

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

1) $$x^3(1-x^2)$$ < 0
$$-x^3(x^2-1$$) < 0
$$x^3(x^2-1)$$ > 0
$$x^3(x-1)(x+1)$$ > 0
x = (-1,0) U (1, oo)
Insufficient.

2) $$x^2-1$$ <0
(x-1)(x+1) < 0
x = (-1,1)
Insufficient.

1) & 2)
$$x^3(x^2-1)$$ > 0
Since $$(x^2-1)$$ is a negative number
$$x^3$$ * [negative number] > 0
$$x^3$$ must be a negative number also.
Therefore, x < 0.

Re: Algebra Arithmetic Operations + Inequalities   [#permalink] 08 Oct 2008, 11:24
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# Data sufficiency (OG) Is x negative? 1) x^3(1-x^2)<0 2)

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