The price of a microchip declines by 67 percent every 6 months. At thi : GMAT Problem Solving (PS)
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# The price of a microchip declines by 67 percent every 6 months. At thi

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

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09 Jul 2007, 17:57
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Question Stats:

54% (02:34) correct 46% (01:38) wrong based on 181 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, 05:46, edited 1 time in total. Renamed the topic, edited the question and added the OA. Director Joined: 26 Feb 2006 Posts: 904 Followers: 4 Kudos [?]: 107 [1] , given: 0 Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink] ### Show Tags 09 Jul 2007, 18:07 1 This post received KUDOS 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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09 Jul 2007, 20:37
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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10 Jul 2007, 08:17
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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10 Jul 2007, 08:29
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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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: 384 Followers: 3 Kudos [?]: 13 [3] , given: 0 Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink] ### Show Tags 10 Jul 2007, 09:51 3 This post received KUDOS I think the fastest way is 81 *(1/3)^n = 1 n =4 So 2 yrs CIO Joined: 09 Mar 2003 Posts: 463 Followers: 2 Kudos [?]: 58 [1] , given: 0 Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink] ### Show Tags 10 Jul 2007, 11:46 1 This post received KUDOS 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: 67 Followers: 1 Kudos [?]: 41 [0], given: 0 Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink] ### Show Tags 10 Jul 2007, 12:12 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. GMAT Club Legend Joined: 09 Sep 2013 Posts: 13464 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink] ### Show Tags 25 Oct 2014, 08:39 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 13464 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink] ### Show Tags 19 Nov 2015, 23:16 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8304 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 381 Kudos [?]: 2465 [0], given: 163 Re: The price of a microchip declines by 67 percent every 6 months. At thi [#permalink] ### Show Tags 29 Nov 2015, 11:00 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

[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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23 Sep 2016, 02:50
(1/3)^x*81=1

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

x=4 and 4/2=2

B
Re: The price of a microchip declines by 67 percent every 6 months. At thi   [#permalink] 23 Sep 2016, 02:50
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