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The price of a microchip declines 67% every 6 months. At

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Intern
Joined: 10 Aug 2007
Posts: 22
The price of a microchip declines 67% every 6 months. At [#permalink]

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23 Nov 2007, 02:49
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The price of a microchip declines 67% every 6 months. At this rate, approximately how many years will it take for the price of a $81 microchip to reach$1?

a.1.5
b.2
c.3
d.13
e.13.5
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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23 Nov 2007, 04:06
2 year.

p1=p0*0.33 ==> pn=p0*(0.33)^n ==>
pn/p0=0.33^n<(0.(3))^n =(1/3)^n

1/81 < 1/3^n

n=4
VP
Joined: 08 Jun 2005
Posts: 1145

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23 Nov 2007, 04:32
the formula is

X = Amount at begining.

N = No of periods

X*((1/3)^N) ---> since 1^N = 1 then X*(1/3^N)

solve

X = 81 = 3^4

3^4 * (1/3^N) = 1

3^4/3^N = 1

3^(4-N) = 1

N has to be 4 since 3^0 = 1

4*6/12 = 2 ---> two years

VP
Joined: 08 Jun 2005
Posts: 1145

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23 Nov 2007, 04:37
Faster way

81/3 = 27
27/3 = 9
9/3 = 3
3/3 = 1

Senior Manager
Joined: 06 Aug 2007
Posts: 361

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23 Nov 2007, 21:41
alohagirl wrote:
The price of a microchip declines 67% every 6 months. At this rate, approximately how many years will it take for the price of a $81 microchip to reach$1?

a.1.5
b.2
c.3
d.13
e.13.5

Here is another way

1 = 81 (1 - 67/100)^2n

1/81 = (1/3)^2n

when n = 2 ==>

(1/3)^4 = 1/81

Hence n = 2 years.
Re: PS-Declining Price   [#permalink] 23 Nov 2007, 21:41
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