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# Is x negative?

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Is x negative? [#permalink]  21 Dec 2009, 12:01
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Difficulty:

55% (hard)

Question Stats:

54% (02:39) correct 46% (01:34) wrong based on 57 sessions
Is x negative?

(1) x^3(1-x^2) < 0
(2) x^2-1 < 0
[Reveal] Spoiler: OA
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Re: Need Help with OG 11 ed DS 154 [#permalink]  21 Dec 2009, 14:12
1
KUDOS
Expert's post
gi wrote:
Hi All,

I'm new to this forum. I'm working through some OG DS questions and I find that some of the explanations to ans are not clear or take too long to solve in 2 mins.

Q:DS154
Is x negative?
1) x^3(1-x^2) < 0
2) x^2-1 < 0

Thanks

(1) $$x^3(1-x^2)<0$$, two cases (one of the multiples negative, another positive):

A. $$x^3>0$$ and $$1-x^2<0$$;

$$x^3>0$$ --> $$x>0$$
----------------0----------------

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

Hence the range for A is $$x>1$$.

B. $$x^3<0$$ and $$1-x^2>0$$

$$x^3<0$$ --> $$x<0$$
---------------0------------

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

Hence the range for B is $$-1<x<0$$.

Two ranges: $$x>1$$ OR $$-1<x<0$$. Not sufficient.

(2) $$x^2-1 < 0$$ --> $$-1<x<1$$. Not sufficient.

(1)+(2) Inersection of the ranges from (1) and (2) is $$-1<x<0$$, hence $$x<0$$ is true. Sufficient.

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Re: Need Help with OG 11 ed DS 154 [#permalink]  21 Dec 2009, 14:21
IMO C:

A) X^2(1-X^2) <0 so X^3<0 or X^2>1
x could be positive or negative

B) X^2-1<0
(X-1)(X+1)<0 so X<1 or X<-1
x could be positive or negative

Combined X is negative for both statements to hold true.

OA?
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Re: Need Help with OG 11 ed DS 154 [#permalink]  21 Dec 2009, 14:33
C; like Bunuel's details.
Inequalities without coffee can not be so much fun!!!

Bunuel,

What subject that you dont like in GMAT Maths?
Be warned, I may too know the answer...!
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Posts: 29776
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Re: Need Help with OG 11 ed DS 154 [#permalink]  21 Dec 2009, 14:52
2
KUDOS
Expert's post
DestinyChild wrote:
C; like Bunuel's details.
Inequalities without coffee can not be so much fun!!!

Bunuel,

What subject that you dont like in GMAT Maths?
Be warned, I may too know the answer...!

Some word problems make me nervous, as I'm not a native English speaker.
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Re: Need Help with OG 11 ed DS 154 [#permalink]  22 Dec 2009, 06:26
IMO C:

A) X^2(1-X^2) <0 so X^3<0 or X^2>1
x could be positive or negative

B) X^2-1<0
(X-1)(X+1)<0 so X<1 or X<-1
x could be positive or negative

Combined X is negative for both statements to hold true.

OA?

Yes the ans is C. Thanks
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Re: Is x negative? [#permalink]  17 Jul 2014, 02:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is x negative?   [#permalink] 17 Jul 2014, 02:34
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