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# The price of a chip falls by approximately 67% every year

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Intern
Joined: 09 Mar 2013
Posts: 10
Location: India
The price of a chip falls by approximately 67% every year  [#permalink]

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16 May 2013, 23:23
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The price of a chip falls by approximately 67% every year. In approximately how many years will the price of an \$81 chip become \$1?

I got his question in a document and it doesnt contain any options. Can you help me to resolve this.
Math Expert
Joined: 02 Sep 2009
Posts: 52295
Re: The price of a chip falls by approximately 67% every year  [#permalink]

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16 May 2013, 23:33
3
rohanchowdhary wrote:
The price of a chip falls by approximately 67% every year. In approximately how many years will the price of an \$81 chip become \$1?

I got his question in a document and it doesnt contain any options. Can you help me to resolve this.

67%=~2/3, which means that the price of a chip becomes 1/3 of the price in a year.

In 1 year the price will be 81*1/3=\$27;
In 2 year the price will be 27*1/3=\$9;
In 3 year the price will be 9*1/3=\$3;
In 4 year the price will be 3*1/3=\$1.

Hope it helps.
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Re: The price of a chip falls by approximately 67% every year  [#permalink]

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16 May 2013, 23:52
+1 Kudos Brunel.

I never though in this way, this si a new way i can drive on to my result.
Intern
Joined: 04 May 2013
Posts: 16
Location: Azerbaijan
Concentration: Finance, General Management
GMAT 1: 710 Q49 V38
Re: The price of a chip falls by approximately 67% every year  [#permalink]

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22 May 2013, 06:55
2
P0 = 81 (price of the chip at 0 moment)
P1 = 1/3 * P0 (67% price decrease means new price = 1/3 of the old price)
P(k+1) = P0 * (1/3)^k
81 * (1/3) ^ k = 1 leads to (1/3)^k = 1/81 = (1/3)^4 so k = 4
CEO
Joined: 11 Sep 2015
Posts: 3341
Re: The price of a chip falls by approximately 67% every year  [#permalink]

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22 Oct 2015, 10:45
1
Bunuel is using something I call a Growth Table approach. So, rather than trying to formulate the correct answer at once, we can just take the time to list successive values until we get to where we need to be.

For more on this, check out our free video - http://www.gmatprepnow.com/module/gmat- ... /video/929
Afterwards, you can practice with this question - http://www.gmatprepnow.com/module/gmat- ... /video/930

Cheers,
Brent
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Director
Joined: 23 Jan 2013
Posts: 559
Schools: Cambridge'16
Re: The price of a chip falls by approximately 67% every year  [#permalink]

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27 Oct 2015, 22:13
we need to find membership in Geometric progression

1 - searched number
81 - first term
1/3 - r (common ratio)

1=81*1/3^(n-1)
1/3^(n-1)=1/81

n-1=4 meaning that 1 will come after 4th year
Director
Joined: 27 May 2012
Posts: 667
Re: The price of a chip falls by approximately 67% every year  [#permalink]

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11 Feb 2018, 07:09
Temurkhon wrote:
we need to find membership in Geometric progression

1 - searched number
81 - first term
1/3 - r (common ratio)

1=81*1/3^(n-1)
1/3^(n-1)=1/81

n-1=4 meaning that 1 will come after 4th year

In the method above it takes 5 years for the price to be \$1 ,

whereas according to expert(s) in 4th year the price will be \$1.

Why is there a mismatch between the G.P way and the Growth table approach , can anybody clear the confusion here?
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Re: The price of a chip falls by approximately 67% every year &nbs [#permalink] 11 Feb 2018, 07:09
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