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# Is x^4-x^3+x^2-x>0? 1) x>1 2) |x^3|>|x|

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Joined: 14 Nov 2016
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Is x^4-x^3+x^2-x>0? 1) x>1 2) |x^3|>|x|  [#permalink]

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09 Mar 2017, 21:45
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55% (hard)

Question Stats:

61% (01:58) correct 39% (01:52) wrong based on 149 sessions

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Is $$x^4-x^3+x^2-x>0$$?

1) $$x>1$$

2) $$|x^3|>|x|$$

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Re: Is x^4-x^3+x^2-x>0? 1) x>1 2) |x^3|>|x|  [#permalink]

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09 Mar 2017, 23:11
ziyuen wrote:
Is $$x^4-x^3+x^2-x>0$$?

1) $$x>1$$

2) $$|x^3|>|x|$$

I chose D,

1- I tried substituting values and found out the bigger x gets, the greater positive number ends up being the result.
2- This rules out x being 0 or being a fraction and I figure this may just be the only way for x not being > 0. However I could not put my finger on exactly how to prove that. Can someone please explain this further on how 2 is helping us in this respect.
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Re: Is x^4-x^3+x^2-x>0? 1) x>1 2) |x^3|>|x|  [#permalink]

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09 Mar 2017, 23:39
$$x^4-x^3+x^2-x>0$$
or $$x(x+1)(x-1)^2 >0$$ therefore x <-1 or x>0

St 1: x>1. it will be positive as for x>0 it is positive and the condition holds true.
St 2: $$|x^3|>|x|$$
condition holds true for x>1 and x<-1. holds true as the values satisfying this equation are the subset for the above question statement

Option D
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Re: Is x^4-x^3+x^2-x>0? 1) x>1 2) |x^3|>|x|  [#permalink]

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11 Jun 2017, 13:21
1
1
hazelnut wrote:
Is $$x^4-x^3+x^2-x>0$$?

1) $$x>1$$

2) $$|x^3|>|x|$$

I solved this as follows:
Statement can be simplified to $$x^4-x^3+x^2-x = (x^3+x)(x-1)$$
$$(x^3+x)(x-1)>0$$ goes to proof that $$(x^3+x)$$ and $$(x-1)$$ have the same sign (both pos or both neg), AND $$x$$ is not 0 or 1.

1) $$x>1$$, implies that $$x-1>0$$ and $$x#0$$, and $$x^3+x>1>0$$ =>Sufficient.

2) $$|x^3|>|x|$$ implies that $$x#0, x#1$$ and $$x#-1$$, and since $$|x|$$ is positive, we can divide both sides by $$|x|$$ without changing the inequation, yielding
$$\frac{|x^3|}{|x|}>1$$ or $$|x^2|>1$$. This means $$x>1$$ or $$x<-1$$.
If $$x>1$$, we are back to statement one => Sufficient
If $$x<-1$$, $$x-1<0$$ and $$x^3+x>1<0$$ =>Sufficient.
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Re: Is x^4-x^3+x^2-x>0? 1) x>1 2) |x^3|>|x|  [#permalink]

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16 Aug 2018, 13:06
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^4-x^3+x^2-x>0? 1) x>1 2) |x^3|>|x| &nbs [#permalink] 16 Aug 2018, 13:06
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