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

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If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]  20 Apr 2012, 20:05
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Apr 2012, 00:11, edited 1 time in total.
Edited the question and added the OA
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Re: Inequalities [#permalink]  21 Apr 2012, 00:10
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gmattest27 wrote:
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?

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}.

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}.

Hope it's clear.
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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]  21 Apr 2012, 07:01
gmattest27 wrote:
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

substitution method.....

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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2))   [#permalink] 21 Apr 2012, 07:01
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