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

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0  [#permalink]

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23 Sep 2018, 22:25
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Is x negative?

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

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

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Re: Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0  [#permalink]

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24 Sep 2018, 04:43
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Bunuel wrote:
Is x negative?

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

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

Question: Is x negative?

Please check the attachment for detailed solution.

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Joined: 12 Mar 2018
Posts: 1
Re: Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0  [#permalink]

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17 Jan 2019, 17:25
1
Bunuel wrote:
Is x negative?

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

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

Hi Bunuel, This is my first post, but I've been on GMAT club for quite a while. Usually my questions get answered by others so I typically don't have to post, but I am completely lost here. Do you have a moment to walk me through this one?
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Joined: 22 Sep 2018
Posts: 249
Re: Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0  [#permalink]

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08 Feb 2019, 22:12
Bunuel wrote:
Is x negative?

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

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

My reasoning:

Statement 1: either $$x^3$$ is negative or $$(1 - x^2)$$ is negative. They are opposite signs. However we can have a positive x and a negative x in this case.

Testing values of 2 and $$\frac{-1}{3}$$ will prove this.

Statement 2: $$x^2 - 1 < 0$$ -> $$x^2 < 1$$ so $$x > -1 & x < 1$$ Again inconclusive because we can have any positive or negative fraction.

Combining the two statements only "negative fractions" are in our overlapping set. The answer is C. x MUST be less than 0
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Joined: 21 Jul 2018
Posts: 194
Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0  [#permalink]

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11 Mar 2019, 06:46
Hi chetan2u, Bunuel, Gladiator59

I am not able to figure out how we are able to find solution combining both the statement for above question, Could you please assist.
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Posts: 7688
Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0  [#permalink]

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11 Mar 2019, 07:00
1
Gmatprep550 wrote:
Hi chetan2u, Bunuel, Gladiator59

I am not able to figure out how we are able to find solution combining both the statement for above question, Could you please assist.

The question is
Quote:
Is x negative?

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

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

Let us take both combined..

Statement II tells us $$x^2 - 1 < 0$$, so when we multiply this with -1, the inequality sign will change
=>$$-1(x^2 - 1) > 0*(-1).....1-x^2>0$$ We did this to get the term of statement I..

Now take statement I..
$$x^3(1 - x^2) < 0$$ ... Here we see from statement II that $$1-x^2>0$$, so $$x^3(1 - x^2) < 0$$ => $$x^3(positive..value) < 0$$ , thus $$x^3<0...x<0$$
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Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0   [#permalink] 11 Mar 2019, 07:00
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# Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0

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