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

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Senior Manager
Joined: 04 Jun 2007
Posts: 374
Followers: 1

Kudos [?]: 12 [0], given: 0

The price of a microchip declines by 67% every 6 months. At [#permalink]  09 Jul 2007, 17:57
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The price of a microchip declines by 67% every 6 months. At this rate approx. how many years will it take for an \$81 chip to reach \$1?

what's the fastest way to do this problem?

this is how i did it-

81- 67% * 81 = 27 approx
27 - 0.67*27 = 9 approx
9- 0.67*9 = 3 approx
3-0.67*3= \$1 approx

hence, 24 months = 2 yrs

is there a faster way??
Director
Joined: 26 Feb 2006
Posts: 908
Followers: 3

Kudos [?]: 36 [0], given: 0

Re: PS from 800score- fastest way to do an easy % problem [#permalink]  09 Jul 2007, 18:07
r019h wrote:
The price of a microchip declines by 67% every 6 months. At this rate approx. how many years will it take for an \$81 chip to reach \$1?

what's the fastest way to do this problem?

this is how i did it-

81- 67% * 81 = 27 approx
27 - 0.67*27 = 9 approx
9- 0.67*9 = 3 approx
3-0.67*3= \$1 approx

hence, 24 months = 2 yrs

is there a faster way??

not sure whether you like this:

81 - (81 x 67%) / 3 = 81 - (81 x 2) / 3 = 27 = 81 / 3

1 = 81 / (3x3x3x3) = 81 / 3^4

so the time = 4 x 6 months = 24 months or 2 years.
Senior Manager
Joined: 04 Jun 2007
Posts: 374
Followers: 1

Kudos [?]: 12 [0], given: 0

i think it should be safe to use 60% (2/3) instead of 67% since the question says approximately.....that will reduce time spent....
Senior Manager
Joined: 04 Jun 2007
Posts: 374
Followers: 1

Kudos [?]: 12 [0], given: 0

wudy wrote:
r019h wrote:
i think it should be safe to use 60% (2/3) instead of 67% since the question says approximately.....that will reduce time spent....

Himalayan's solution is better.

not getting this part though-

81 - (81 x 67%) / 3 = 81 - (81 x 2) / 3 = 27 = 81 / 3 <--why did you replace the 67% with 2??
Manager
Joined: 07 Feb 2007
Posts: 212
Followers: 1

Kudos [?]: 6 [0], given: 0

r019h wrote:
wudy wrote:
r019h wrote:
i think it should be safe to use 60% (2/3) instead of 67% since the question says approximately.....that will reduce time spent....

Himalayan's solution is better.

not getting this part though-

81 - (81 x 67%) / 3 = 81 - (81 x 2) / 3 = 27 = 81 / 3 <--why did you replace the 67% with 2??

You are right.
I thought Himalayan made a typo. She tries to find out the leftover.
It should be "81 - (81 x 67%) = 81 - (81 x 2) / 3 = 27 = 81 / 3"
Director
Joined: 26 Feb 2006
Posts: 908
Followers: 3

Kudos [?]: 36 [0], given: 0

Re: PS from 800score- fastest way to do an easy % problem [#permalink]  10 Jul 2007, 08:57
Himalayan wrote:
r019h wrote:
The price of a microchip declines by 67% every 6 months. At this rate approx. how many years will it take for an \$81 chip to reach \$1?

what's the fastest way to do this problem?

this is how i did it-

81- 67% * 81 = 27 approx
27 - 0.67*27 = 9 approx
9- 0.67*9 = 3 approx
3-0.67*3= \$1 approx

hence, 24 months = 2 yrs

is there a faster way??

not sure whether you like this:

81 - (81 x 67%)/3 = 81 - (81 x 2) / 3 = 27 = 81 / 31 = 81 / (3x3x3x3) = 81 / 3^4

so the time = 4 x 6 months = 24 months or 2 years.

you guys are correct.
there was a typo, it should be:

81 - (81 x 67%) = 81 - (81 x 2) / 3 = 27 = 81 / 3
Senior Manager
Joined: 03 Jun 2007
Posts: 385
Followers: 2

Kudos [?]: 8 [0], given: 0

I think the fastest way is

81 *(1/3)^n = 1
n =4
So 2 yrs
CIO
Joined: 09 Mar 2003
Posts: 466
Followers: 1

Kudos [?]: 23 [0], given: 0

Just divide 81 by 3 as many times as necessary to hit 1. It can't take more than 21 seconds to get the answer.
Manager
Joined: 11 Jul 2006
Posts: 68
Followers: 1

Kudos [?]: 7 [0], given: 0

i think the key to this question is notice that:

(1-67%) = 1-2/3 = 1/3

Then divide 81/3 until it hits 1.
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