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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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New post Updated on: 05 Mar 2016, 18:43
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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) \(x = 2y\)

Originally posted by tonebeeze on 19 Oct 2010, 11:15.
Last edited by ENGRTOMBA2018 on 05 Mar 2016, 18:43, 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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New post 19 Oct 2010, 11:23
1
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.

Answer: A.

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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New post 19 Oct 2010, 13:29
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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New post 15 Oct 2013, 09:06
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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New post 05 Mar 2016, 18:38
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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New post 08 Mar 2016, 20:36
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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New post 18 Sep 2016, 08:53
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
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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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