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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, 19:05
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Question Stats:

77% (02:27) correct 22% (01:29) wrong based on 79 sessions
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 20 Apr 2012, 23:11, edited 1 time in total.
Edited the question and added the OA
Math Expert
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Re: Inequalities [#permalink]  20 Apr 2012, 23:10
3
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Expert's post
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 Jun 2013, 02:48
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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]  22 Jun 2013, 00:53
1
KUDOS
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

We just need to find the factor thats all,

x-> doubled -> 2x
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2

W is in numerator, and x*z in denominator.

Hence,
Additional factor being introduced = 4/2*9

=4/18 = 2/9 = B
_________________

Re: If the function Q is defined by the formula Q = 5w/(4x(z^2))   [#permalink] 22 Jun 2013, 00:53
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