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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]  19 Oct 2010, 11:15
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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
[Reveal] Spoiler: OA
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Re: Difficult Algebra DS Problem from Past GMAT ETS paper exam [#permalink]  19 Oct 2010, 11:23
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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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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
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Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
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Re: Difficult Algebra DS Problem from Past GMAT ETS paper exam [#permalink]  19 Oct 2010, 13:29
Thanks Bunuel. I apologize for the bad formatting. Won't happen again!
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Re: Difficult Algebra DS Problem from Past GMAT ETS paper exam [#permalink]  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]  29 Jan 2016, 03:49
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Re: If xy does not equal 0, what is the value of ((x^2)^3 y^4)/x   [#permalink] 29 Jan 2016, 03:49
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