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# If x≠0, is -4/x^3 negative?

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Ryerson (Ted Rogers) Thread Master
Joined: 27 Sep 2015
Posts: 57
Location: Canada
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.

_________________

Discipline does not mean control. Discipline means having the sense to do exactly what is needed.

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Joined: 02 Sep 2009
Posts: 50009
If x≠0, is -4/x^3 negative?  [#permalink]

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21 Dec 2015, 09:25
1
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
Joined: 27 Sep 2015
Posts: 57
Location: Canada
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.

Answer: D.

Hope it's clear.

Thanks. You got KUDO, as my token of appreciation.
_________________

Discipline does not mean control. Discipline means having the sense to do exactly what is needed.

Manager
Joined: 10 Apr 2018
Posts: 152
Re: If x≠0, is -4/x^3 negative?  [#permalink]

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 50009
Re: If x≠0, is -4/x^3 negative?  [#permalink]

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14 Aug 2018, 00:49
1
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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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.
If x≠0, is -4/x^3 negative? &nbs [#permalink] 15 Aug 2018, 10:12
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# If x≠0, is -4/x^3 negative?

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