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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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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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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]

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22 Jun 2013, 01:53
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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,

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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21 Jun 2013, 03:48
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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!

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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16 Jul 2014, 23:06
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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16 Jul 2014, 23:54
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 = $$\frac{4}{2*9} = \frac{2}{9}$$

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

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20 Feb 2017, 19:09
I don't understand how Bunuel gets 18 in the denominator in the third step.
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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]

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20 Feb 2017, 23:59
Nunuboy1994 wrote:
I don't understand how Bunuel gets 18 in the denominator in the third step.

4*2x*9*z^2 = 18*(4x*z^2).
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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2))   [#permalink] 20 Feb 2017, 23:59
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