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The price of a microchip declines by 67 percent every 6 months. At thi

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The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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Question Stats:

61% (01:28) correct 39% (01:39) wrong based on 209 sessions

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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 reach $1?

A. 1.5 years
B. 2 years
C. 3 years
D. 13 years
E. 13.5 years

[Reveal] Spoiler:
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??
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Oct 2014, 06:46, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 09 Jul 2007, 19:07
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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.

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 09 Jul 2007, 21:37
i think it should be safe to use 60% (2/3) instead of 67% since the question says approximately.....that will reduce time spent....

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 10 Jul 2007, 09:17
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??

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 10 Jul 2007, 09:29
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"

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 10 Jul 2007, 09:57
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

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 10 Jul 2007, 10:51
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I think the fastest way is

81 *(1/3)^n = 1
n =4
So 2 yrs

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 10 Jul 2007, 12:46
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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.

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 10 Jul 2007, 13:12
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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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 29 Nov 2015, 12:00
Hi All,

This question is really just about fractions and basic arithmetic, so you don't need a 'fancy' approach to solve it - you just need to do the necessary work on the pad.

We're told to start with an $81 microchip and that its price reduces by about 2/3 every 6 months. We're asked how long it takes for that chip to get to a $1 price. A few calculations should be all that's required to get to the answer:

Start: $81

Reducing this price by 2/3 means that 1/3 of the price will be left:
(1/3)(81) = 27
The price 6 months later is $27

We can repeat this same set of 'steps' again...
(1/3)(27) = 9
The price 12 months later is $9

(1/3)(9) = 3
The price 18 months later is $3

(1/3)(3) = 1
The price 24 months later is $1

Final Answer:
[Reveal] Spoiler:
B


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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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New post 23 Sep 2016, 03:50
(1/3)^x*81=1

(1/3)^x=1/81 or (1/3)^x=(1/3)^4

x=4 and 4/2=2

B

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Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink]

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Re: The price of a microchip declines by 67 percent every 6 months. At thi   [#permalink] 10 Oct 2017, 07:29
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