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# Is x^4-x>0?

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Manager
Joined: 03 Oct 2016
Posts: 79
Concentration: Technology, General Management
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21 Oct 2016, 10:03
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Difficulty:

55% (hard)

Question Stats:

57% (01:50) correct 43% (01:29) wrong based on 180 sessions

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Is $$x^{4}$$ - x >0 ?

1) x<0
2) $$x^{4} > x^{2}$$

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21 Oct 2016, 10:45
idontknowwhy94 wrote:
Is $$x^{4}$$ - x >0 ?

1) x<0
2) $$x^{4} > x^{2}$$

Rephrasing
x(x^3-1)>0
----> x<0 or x>1??

1) x<0 ---->suff
2)x^2(x^2-1)>0
x^2(x+1)(x-1)>0
thus -1<x<0 or x>1------->suff

Ans D
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21 Oct 2016, 21:02
1
idontknowwhy94 wrote:
Is $$x^{4}$$ - x >0 ?

1) x<0
2) $$x^{4} > x^{2}$$

Is $$x^{4}$$ - x >0 --> Is $$x^4 > x$$ ?

St1: x < 0 --> x^4 is positive and x is negative. --> x^4 > x. Sufficient

St2: $$x^{4} > x^{2}$$ --> If x^4 > x^2 then x^4 > x. Sufficient

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21 Oct 2016, 21:14
idontknowwhy94 wrote:
Is $$x^{4}$$ - x >0 ?

1) x<0
2) $$x^{4} > x^{2}$$

Question: Is $$x^{4}$$ - x >0 ?

Here I am solving this question in more of logical approach rather than using more of Maths

x^4 will be greater than x only if
i) x>1 or
ii) x<0 or

Statement 1: x<0
SUFFICIENT

Statement 2: $$x^{4} > x^{2}$$
which is true only if
i) x>1 or
ii) x<-1 hence
SUFFICIENT

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22 Oct 2016, 01:15
idontknowwhy94 wrote:
Is $$x^{4}$$ - x >0 ?

1) x<0
2) $$x^{4} > x^{2}$$

from stem is x(x^3-1)>0 true if x>1 or x<0 ...

from 1

x<0 ... suff

from 2

x^2(x^2-1) >0 , thus /x/>1, i.e. x<-1( X<0) or x>1 ..... suff

D
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Joined: 03 Sep 2018
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15 Jan 2019, 09:24
are we allowed to solve the second statement as follows:

$$x^4>x^2$$ $$\implies$$ $$x^2>0$$ $$\implies$$ $$x>0$$?
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15 Jan 2019, 09:43
idontknowwhy94 wrote:
Is $$x^{4}$$ - x >0 ?

1) x<0
2) $$x^{4} > x^{2}$$

$$x^{4}$$ - x > 0
$$x^{4}$$ will always be positive and for that inequality to be !> 0 , x has to be 1

1) x<0
this will take -ive values, which will always satisfy the original question.

2) $$x^{4} > x^{2} [m]x^{4} - x^{2}$$ > 0
$$x^{2}(x^{2} - 1)$$ > 0
$$x^{2}$$ will always be > 0, which means $$(x^{2}$$ > 1, this will take + ive values > than 1 , which will always satisfy the original question.

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Re: Is x^4-x>0?   [#permalink] 15 Jan 2019, 09:43
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