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If x≠0, is -4/x^3 negative?

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Ryerson (Ted Rogers) Thread Master
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If x≠0, is -4/x^3 negative? [#permalink]

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New post 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.
Spoiler: OA

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If x≠0, is -4/x^3 negative? [#permalink]

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New post 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.

Answer: D.

Hope it's clear.
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Ryerson (Ted Rogers) Thread Master
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Re: If x≠0, is -4/x^3 negative? [#permalink]

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New post 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.

Answer: D.

Hope it's clear.


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

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