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If the function Q is defined by the formula Q = 5w/4xz^2 , by what factor will Q be multi-plied if w is quadrupled, x is doubled, and z is tripled?

Please help explain this ..

Thanks in advance

If the function Q is defined by the formula Q = 5w/(4x(z^2)), by what factor will Q be multiplied if w is quadrupled, x is doubled, and z is tripled? A. 1/9 B. 2/9 C. 4/9 D. 3/9 E. 2/27

Given: \(Q=\frac{5w}{4x*z^2}\).

Now, quadruple \(w\), so make it \(4w\); double \(x\) so make it \(2x\); triple \(z\) and substitute these values instead of \(x\), \(y\), and \(z\) in the original equation:

\(\frac{5(4w)}{4(2x)*(3z)^2}=\frac{4*5w}{4*2x*9*z^2}=\frac{4*5w}{18*(4x*z^2)}=\frac{4}{18}*\frac{5w}{4x*z^2}=\frac{2}{9}*\frac{5w}{4x*z^2}\). Thus Q is multiplied by \(\frac{2}{9}\).

Answer: B.

Else plug-in values for \(x\), \(y\), and \(z\). Let \(x=y=z=1\) --> \(Q=\frac{5w}{4x*z^2}=\frac{5}{4}\).

\(4w=4\), \(2x=2\) and \(3z=3\) --> \(\frac{5*4}{4*2*3^2}=\frac{4}{18}*\frac{5}{4}=\frac{2}{9}*\frac{5}{4}\). Thus Q is multiplied by \(\frac{2}{9}\).

Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]

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16 Jul 2014, 21:37

Hello from the GMAT Club BumpBot!

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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]

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06 Jan 2017, 12:47

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]

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09 Jan 2017, 15:53

Just understand words Quadrupled = 4 times Q = \(\frac{5w}{4x z^{2}}\) \(\frac{5 x 4w}{4(2x) . (3z)^{2}}\) Take out Q factor \(\frac{4}{18}\) \(\frac{2}{9}\) B
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