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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 11 Dec 2012, 01:00, edited 3 times in total.
Edited the question and added the answer choices with OA
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Re: Direct and inverse proportionality [#permalink]

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New post 04 Jun 2011, 18:09
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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: Direct and inverse proportionality [#permalink]

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New post 22 Feb 2012, 23:08
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SergeNew wrote:
Hi guys,

I am sorry, but i still did not get this part.


Q'=5w/18xz²
to
Q'=2/9*(5w/4xz²)

Would anyone be able please to elaborate on it? I would really appreciate it.


Serge.


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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New post 10 Dec 2012, 21:16
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\(Q=\frac{{5w}}{{4xz^2}}\)

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

Answer: 2/9
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Re: Direct and inverse proportionality [#permalink]

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New post 06 Jun 2011, 00:34
According to expression Q= 5w/4xz²
now, w'=4w,
x'=2x
z'=3z
Put these values in a same order, we get
Q'= 5(4w)/4(2x)(3z)²
Q'=5w/18xz²
Q'=2/9*(5w/4xz²)
So, Q'= 2/9(Q),q will be a multiple of factor 2/9.
This is the most effective way to solve such question. 8-)
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Re: Direct and inverse proportionality [#permalink]

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New post 11 Jun 2011, 16:32
\(Q = 5W/(4XZ^2)\)

Q1 = \(5(2W)/(4(2X)9X^2)\) = 2/9 Q

So the factor is 2/9.
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Re: Direct and inverse proportionality [#permalink]

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New post 22 Feb 2012, 22:49
Hi guys,

I am sorry, but i still did not get this part.


Q'=5w/18xz²
to
Q'=2/9*(5w/4xz²)

Would anyone be able please to elaborate on it? I would really appreciate it.


Serge.
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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 20 Dec 2012, 14:20
Isn't the tag wrong. It doesnt seem like a 700-level question
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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] 19 Sep 2016, 23:17
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