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Intern  Joined: 24 Feb 2011
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If the function Q is defined by the formula Q = 5w/(4x(z^2)), by what  [#permalink]

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If the function Q is defined by the formula $$Q = \frac{5w}{4x(z^2)}$$, 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

Originally posted by olivite on 04 Jun 2011, 12:33.
Last edited by Bunuel on 09 Sep 2019, 03:57, edited 4 times in total.
Edited the question and added the answer choices with OA
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If the function Q is defined by the formula Q = 5w/(4x(z^2)), by what  [#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

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)), by what  [#permalink]

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IN the expression Q=5w/4xz^2, substitute the values as mentioned :

So new expression is -> 5 * (4w)/(4 * (2x) * (3z)^2)

= 5 * w/(2x * 9 * z^2)

= (2/9) * 5w/4xz^2

= 2/9 * Q

So Q will be multiplied by the factor 2/9.
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Re: If the function Q is defined by the formula Q = 5w/(4x(z^2)), by what  [#permalink]

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$$Q=\frac{{5w}}{{4xz^2}}$$

$$Qmod=\frac{{5(4w)}}{{4(2x)(3z)^2}}$$
$$Qmod=\frac{{20w)}}{{72xz^2}}$$
$$Qmod=\frac{4}{18}*\frac{{5w}}{{4xz^2}}$$
$$Qmod=\frac{4}{18}*Q$$
$$Qmod=\frac{2}{9}*Q$$

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

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

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)), by what  [#permalink]

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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)), by what  [#permalink]

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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)), by what  [#permalink]

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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)), by what  [#permalink]

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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)), by what   [#permalink] 09 Sep 2019, 03:58
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