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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.

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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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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.


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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New post 13 Aug 2018, 13:49
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.


Hi Bunuel,

can we safely say that if Cube of a number - square of a number is positive, then that number is positive.
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Re: If x≠0, is -4/x^3 negative?  [#permalink]

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New post 14 Aug 2018, 00:49
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Probus wrote:
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.


Hi Bunuel,

can we safely say that if Cube of a number - square of a number is positive, then that number is positive.


Yes. x^3 - x^2 > 0 is true only if x > 1.
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If x≠0, is -4/x^3 negative?  [#permalink]

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New post 15 Aug 2018, 10:12
Hi Bunuel,
I have a slight query. Could it not be that x^3 - x^2 > 0 instead of > 1.
Even if say x is 1/2, the result would be a negative number. But that negative sign cancels out with the negative sign mentioned in the equation and the result is positive anyway?

I just wanted to make sure so I don't mess up while assuming values for such problems.
Please help!
Thanks :)


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.
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If x≠0, is -4/x^3 negative?   [#permalink] 15 Aug 2018, 10:12
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