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# The useful life of a certain piece of equipment is

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The useful life of a certain piece of equipment is [#permalink]  20 Feb 2008, 15:00
The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment. If the density of the underlying material is doubled and the daily usage of the equipment is halved, what will be the percentage increase in the useful life of the equipment?

300%
400%
600%
700%
800%
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Re: MGMAT - Formula [#permalink]  20 Feb 2008, 15:09
bmwhype2 wrote:
The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment. If the density of the underlying material is doubled and the daily usage of the equipment is halved, what will be the percentage increase in the useful life of the equipment?

300%
400%
600%
700%
800%

if it's h^2 then D is the answer
I really don't like units though
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Re: MGMAT - Formula [#permalink]  20 Feb 2008, 15:09
bmwhype2 wrote:
The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment. If the density of the underlying material is doubled and the daily usage of the equipment is halved, what will be the percentage increase in the useful life of the equipment?

300%
400%
600%
700%
800%

I am assuming your question is u =(8d)/h^2,

Hence new equation would be
u_1 = \frac{8 * (2d)}{(\frac{h}{2})^2} --> u_1 = 8 * \frac{8 * d} {({h})^2} --> u_1 = 8*u

Hence 700% increase....
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Re: MGMAT - Formula [#permalink]  20 Feb 2008, 19:01
agreed. assuming question is h^2, we have:

percentage change = u2-u1/u2 * 100

u1=8d/h^2

u2=[8*2d]/[(h/2)^2] -->64d/h^2

64d/h^2 - 8d/h^2 / 8d/h^2 = 7*100 = 700%
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Re: MGMAT - Formula [#permalink]  21 Feb 2008, 02:42
U = (8d) / h2 without any percentage change
D = 1 h = 1
Uold = 4
With change
Unew = 16d / h
D = 1 h = 1
Unew = 16

400%
Re: MGMAT - Formula   [#permalink] 21 Feb 2008, 02:42
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