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

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

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New post 23 Sep 2018, 22:25
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A
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C
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E

Difficulty:

  65% (hard)

Question Stats:

56% (01:59) correct 44% (01:58) wrong based on 220 sessions

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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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New post 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.

This is how GMATINSIGHT teaches Data sufficiency

Answer: Option C
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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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New post 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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Re: Is x negative? (1) x^3(1 - x^2) < 0 (2) x^2 - 1 < 0  [#permalink]

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

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

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New post 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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