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x(X-1) > 0

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Joined: 14 Nov 2014
Posts: 5
x(X-1) > 0  [#permalink]

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New post 06 Dec 2014, 15:59
Hi
I read a explanation that considered x(x-1) > 0 as X<0 and X >1
Can somebody explain why?
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Re: x(X-1) > 0  [#permalink]

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New post 06 Dec 2014, 21:39
1
Before the solution, I would like to tell you some theory
if we have x*y > 0 or x/y > 0 then that means that
both x and y can be either positive or both can be negative
i.e. both x and y have the same sign
so, we have
x>0, y>0 or x<0,y<0

if we have if you have x*y < 0 or x/y < 0 then that means that
(x can be positive and y will be negative) or (x can be negative and y will be positive)
i.e. x and y have opposite signs
so, we have
x>0, y<0 or x<0,y>0

Coming to the question
x*(x-1) > 0
this is of the form xy>0 i.e. x and y have the same sign
so,
(1) either, x > 0 and x-1 >0
i.e. x >0 or x>1
taking intersection of the two possibilities we have x >1

(2)or x <0, and x-1 < 0
i.e. x <0 or x<1
taking intersection of the two possibilities we have x < 0

So, solution will be x <0 or x>1

You can also go through this post to know how to solve inequalities in detail
gmat-quant-equation-functions-inequalities-formula-sheet-149203.html

Hope it helps!

surenz298 wrote:
Hi
I read a explanation that considered x(x-1) > 0 as X<0 and X >1
Can somebody explain why?

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Re: x(X-1) > 0   [#permalink] 06 Dec 2014, 21:39
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