function Q

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function Q

by GmatKiss » Sun Aug 21, 2011 12:18 am
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?

1/9
2/9
4/9
3/9
2/27
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by Anurag@Gurome » Sun Aug 21, 2011 1:23 am
GmatKiss 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?
Q = 5w/(4xz²)

After quadrupling w, doubling x, and tripling z the new function will be equal to, Q' = 5*(4w)/[4*(2x)*(3z)²] = 4*(5w)/[4*(2x)*(9z²)] = [4/(2*9)]*(5w)/(4xz²) = (4/18)*Q = (2/9)*Q

The correct answer is B.
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by GMATGuruNY » Sun Aug 21, 2011 2:51 am
GmatKiss 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?

1/9
2/9
4/9
3/9
2/27
Let w=4, x=1, and z=1.
Then Q = 5w/(4x(z^2)) = (5*4)/(4*1)(1^2) = 20/4 = 5.

W quadrupled = 4*4 = 16.
X doubled = 2*1 = 2.
Z tripled = 3*1 = 3.
New Q = 5w/(4x(z^2)) = (5*16)/(4*2)(3^2) = 10/9.

New Q/Old Q = (10/9)/5 = 2/9.

The correct answer is B.
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