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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]

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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 20 Apr 2012, 23:11, edited 1 time in total.
Edited the question and added the OA
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Re: Inequalities [#permalink]

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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?

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 \(\frac{2}{9}\).

Answer: B.

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

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

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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,

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

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

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New post 16 Jul 2014, 22:06
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


This is a very simple case of joint variation. Check out this link for a discussion on joint variation: http://www.veritasprep.com/blog/2013/02 ... g-jointly/
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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]

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New post 16 Jul 2014, 22:54
w becomes 4w ......... Resultant = 4

x becomes 2x ............ Resultant = 2

z becomes 3z ............. Resultant \(= 3^2 = 9\) (As z is sitting under a square sign)

Multiplication factor = \(\frac{4}{2*9} = \frac{2}{9}\)

Answer = B
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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2))   [#permalink] 16 Jul 2014, 22:54
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