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# If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x

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If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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19 Oct 2010, 12:15
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If $$xy \neq 0$$, what is the value of $$\frac{((x^2)^3 y^4)}{x}$$?

(1) $$x^3y^5 = \frac{6y}{x^2}$$

(2) $$x = 2y$$
[Reveal] Spoiler: OA

Last edited by Engr2012 on 05 Mar 2016, 19:43, edited 1 time in total.
Reformatted the question
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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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19 Oct 2010, 12:23
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tonebeeze wrote:
Hello all,

Can someone please walk me thru how they best simplified this. Thanks

If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x ?

(1) x^3y^5 = 6y/x^2

(2) x = 2y

$$xy\neq{0}$$ means that neither of unknowns equals to zero.

$$\frac{(x^2)^3*y^4}{x}=\frac{x^6*y^4}{x}=x^5*y^4=?$$

(1) $$x^3y^5=\frac{6y}{x^2}$$ --> multiple by $$x^2$$ --> $$x^5y^5=6y$$ --> reduce by $$y$$ --> $$x^5y^4=6$$. Sufficient.

(2) $$x=2y$$ --> $$x^5*y^4=(2y)^5*y^4=32y^9=?$$ --> need to know the value of $$y$$ (or $$x$$). Not sufficient.

For more on exponents check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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19 Oct 2010, 14:29
Thanks Bunuel. I apologize for the bad formatting. Won't happen again!
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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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15 Oct 2013, 10:06
tonebeeze wrote:
Thanks Bunuel. I apologize for the bad formatting. Won't happen again!

And just to emphasize that we can divide both sides by y ONLY BECAUSE we are explicitly told that x and y are both different from zero as Bunuel clearly explained above.
Cheers

J
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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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29 Jan 2016, 04:49
Hello from the GMAT Club BumpBot!

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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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05 Mar 2016, 19:38
Bunuel - Can you please add the math formula formatting tag to the OP. For the first minute, I was solving for y as a power of x. :l
Thanks!
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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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08 Mar 2016, 21:36
jlgdr wrote:
tonebeeze wrote:
Thanks Bunuel. I apologize for the bad formatting. Won't happen again!

And just to emphasize that we can divide both sides by y ONLY BECAUSE we are explicitly told that x and y are both different from zero as Bunuel clearly explained above.
Cheers

J

You are absolutely right...
if xy≠0 wasn't mentioned then A would be insufficient as y can be zero too.
and hence E would have been the answer..
Thanks
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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x [#permalink]

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18 Sep 2016, 09:53
A is correct. Here's why:

Manipulate orig eq to the following --> (x^5)(y^4) = ?

(1) (x^3)(y^5) = 6y
= (x^5)(y^4) = 6

SUFFICIENT

(2) x = 2y --> plug into orig eq
=(2y)^5[(y^4)] = 32(y^9)

NOT SUFFICIENT
Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x   [#permalink] 18 Sep 2016, 09:53
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