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# If y does not equal 0. Does x = 0 ?

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If y does not equal 0. Does x = 0 ? [#permalink]  06 Jan 2011, 05:32
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If y does not equal 0. Does x = 0 ?

(1) x^2*y = x^3*y
(2) x^2/y = x^3*y
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Oct 2014, 06:55, edited 2 times in total.
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Re: If y does not equal 0. Does x = 0 ? [#permalink]  06 Jan 2011, 05:45
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rxs0005 wrote:
If y <> = 0 Does x = 0

x^2 y = x^3 y

x^2 / y = x^3 y

Given: $$y\neq{0}$$. Question does $$x=0$$?

(1) x^2*y=x^3*y --> as $$y\neq{0}$$ we can reduce by $$y$$ --> $$x^2=x^3$$ --> $$x^2(x-1)=0$$ --> either $$x=0$$ or $$x=1$$. Not sufficient.

(2) x^2/y=x^3*y --> $$x^2=x^3y^2$$ --> $$x^2(xy^2-1)=0$$ --> either $$x=0$$ or $$xy^2=1$$ (depending on $$y$$ $$x$$ can be any positive number). Not sufficient.

(1)+(2) Both $$x=0$$ and $$x=1$$ (in this case $$y=1$$ or $$y=-1$$) satisfy the statements. Not sufficient.

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Re: If y does not equal 0. Does x = 0 ? [#permalink]  07 Sep 2011, 04:19
**
Quote:
If y <> = 0 Does x = 0

(1) x^2 y = x^3 y

(2) x^2 / y = x^3 y

Very clear explanation, Bunuel. Thanks!
Initially, I had answer A and realised my mistake after reading Bunuel's solution. My error came from the fact that I cross-multiplied and eliminated as below:
Quote:
From Statement 1
--> x^2y=x^3y --> y/y = x^3/x^2 --> x = 1
Sufficient

Given y does not equal to zero, does x=0?

Statement 1
x^2y = x^3y --> x^3=x^2 --> 0 = x^2(x-1)
So, x=0 or x=1
Insufficient.

Statement 2
x^2/y = x^3y --> 0 = x^2(xy^2-1)
So, x=0 or xy^2=1 (i.e. x is not zero)
Insufficient.

Statement 1 + 2
x^2(x-1) = x^2(xy^2-1)
x-1 = xy^2-1
x(1-y^2) = 0
So, x = 0 or x does not equals to zero (when y^2=1)
Insufficient.

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Re: If y does not equal 0. Does x = 0 ? [#permalink]  26 Aug 2012, 09:55
Very nice explanation Bunuel , thanks a lot !

I was confused whether to choose D or E because i thought that in either of the options x is coming 0 (along with some other value)

But it suggests that the value is not sufficient in both the cases.
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Re: If y does not equal 0. Does x = 0 ? [#permalink]  29 Dec 2012, 01:21
If y does not equal 0. Does x = 0 ?

(1) x^2 y = x^3 y
(2) x^2 / y = x^3 y

please do calrify my doubt :

Given:
y does not equal to zero, does x=0?

x^2y = x^3y

Here we are calculating as x^2y-x^3y
my question is
why can't we do as x^2y/x^3y

Please do clarify when what is the actual procedure and why can't do like this as mentioned later
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Re: If y does not equal 0. Does x = 0 ? [#permalink]  29 Dec 2012, 02:51
Expert's post
skamal7 wrote:
If y does not equal 0. Does x = 0 ?

(1) x^2 y = x^3 y
(2) x^2 / y = x^3 y

please do calrify my doubt :

Given:
y does not equal to zero, does x=0?

x^2y = x^3y

Here we are calculating as x^2y-x^3y
my question is
why can't we do as x^2y/x^3y

Please do clarify when what is the actual procedure and why can't do like this as mentioned later

Merging similar topics. Please refer to the solutions above.

Next, I guess your question is why are not we dividing both parts of x^2*y = x^3*y by x^3*y to get x^2*y/(x^3*y) = 1. That's because x^3*y can be zero (in case y=0) and we cannot divide by 0.

Hope it's clear.
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Re: If y does not equal 0. Does x = 0 ? [#permalink]  13 Nov 2014, 13:43
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Re: If y does not equal 0. Does x = 0 ?   [#permalink] 13 Nov 2014, 13:43
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