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If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]
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04 Jun 2011, 12:33
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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
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Last edited by Bunuel on 11 Dec 2012, 02:00, 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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04 Jun 2011, 19:09
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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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06 Jun 2011, 01:34
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.



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Re: Direct and inverse proportionality [#permalink]
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11 Jun 2011, 17:32
\(Q = 5W/(4XZ^2)\)
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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22 Feb 2012, 23:49
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: Direct and inverse proportionality [#permalink]
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23 Feb 2012, 00:08
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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 plugin 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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10 Dec 2012, 22:16
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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: If the function Q is defined by the formula Q = 5w/(4x(z^2)) [#permalink]
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20 Dec 2012, 15:20
Isn't the tag wrong. It doesnt seem like a 700level 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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