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# Price of microchip - percentage

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Manager
Joined: 03 Jul 2009
Posts: 106
Location: Brazil
Price of microchip - percentage [#permalink]

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28 Jul 2009, 14:16
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The price of a microchip declines by 67 percent every 6 months. At this rate, approximately how many years will it take for the price of an $81 microchip to drop below$1?

A. 1.5
B. 2
C. 3
D. 13
E. 13.5
Manager
Joined: 10 Jul 2009
Posts: 164
Re: Price of microchip - percentage [#permalink]

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28 Jul 2009, 20:36
As price of the chip declines by 67%, the new price of the chip after 6 months is 33% of the original price.
So price of chip after 6 months = 81/3
Price of chip after n number of 6 months = 81/(3^n)
given 1 = 81/(3^n)
81 = 3^n
n = 4
So number of years = 4*6/12 = 2
Manager
Joined: 30 May 2009
Posts: 216
Re: Price of microchip - percentage [#permalink]

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28 Jul 2009, 20:41
Recognizing that 67% or .67 is close to .66666666 is the key here.
.666666 = 2/3

So once you realize that 67% is 2/3 the problem becomes simple and you will see that B is the answer.
Manager
Joined: 03 Jul 2009
Posts: 106
Location: Brazil
Re: Price of microchip - percentage [#permalink]

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29 Jul 2009, 04:55
OA B

sdrandom1, thank you for the tip. It is faster this way.
Re: Price of microchip - percentage   [#permalink] 29 Jul 2009, 04:55
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