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If x≠0, is -4/x^3 negative?

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Joined: 27 Sep 2015
Posts: 57
GMAT 1: 410 Q33 V13
WE: Management Consulting (Computer Software)
If x≠0, is -4/x^3 negative? [#permalink]

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21 Dec 2015, 09:15
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If $$x≠0$$, is $$-\frac{4}{x^3}$$ negative?

(1) $$x$$ is positive.
(2) $$x^3 - x^2$$ is positive.

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Joined: 02 Sep 2009
Posts: 46284
If x≠0, is -4/x^3 negative? [#permalink]

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21 Dec 2015, 09:25
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If $$x≠0$$, is $$-\frac{4}{x^3}$$ negative?

Notice that the question basically asks whether x is a positive number, because if it is then $$-\frac{4}{x^3} =-(\frac{positive}{positive})=negative$$.

(1) $$x$$ is positive. Directly answers the question. Sufficient.

(2) $$x^3 - x^2$$ is positive --> x^3- x^2 > 0 --> x^3 > x^2 --> reduce by x^2 (we can safely do that because x^2 will be positive): x > 1. The same here: x is positive. Sufficient.

Hope it's clear.
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Joined: 27 Sep 2015
Posts: 57
GMAT 1: 410 Q33 V13
WE: Management Consulting (Computer Software)
Re: If x≠0, is -4/x^3 negative? [#permalink]

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21 Dec 2015, 09:31
Bunuel wrote:
If $$x≠0$$, is $$-\frac{4}{x^3}$$ negative?

Notice that the question basically asks whether x is a positive number, because if it is then $$-\frac{4}{x^3} =-(\frac{positive}{positive})=negative$$.

(1) $$x$$ is positive. Directly answers the question. Sufficient.

(2) $$x^3 - x^2$$ is positive --> x^3- x^2 > 0 --> x^3 > x^2 --> reduce by x^2 (we can safely do that because x^2 will be positive): x > 1. The same here: x is positive. Sufficient.

Hope it's clear.

Thanks. You got KUDO, as my token of appreciation.
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Re: If x≠0, is -4/x^3 negative? [#permalink]

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22 Oct 2017, 09:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x≠0, is -4/x^3 negative?   [#permalink] 22 Oct 2017, 09:09
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