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

Question

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.

Bunuel · Answer

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.

rohanchowdhary · Answer

+1 Kudos Brunel.

I never though in this way, this si a new way i can drive on to my result.

VadimKlimenko · Answer

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

BrentGMATPrepNow · Answer

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 - https://www.gmatprepnow.com/module/gmat- ... /video/929
Afterwards, you can practice with this question - https://www.gmatprepnow.com/module/gmat- ... /video/930

Cheers,
Brent

Temurkhon · Answer

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

stne · Answer

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?

bumpbot · Answer

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

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

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