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If the price of steak is currently $1.00 a pound, and the price triple

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If the price of steak is currently $1.00 a pound, and the price triple  [#permalink]

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New post 22 Oct 2017, 05:16
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If the price of steak is currently $1.00 a pound, and the price triples every 6 months, how long will it be until the price of steak is $81.00 a pound?

(A) 1 year
(B) 2 years
(C) 5/2 years
(D) 13 years
(E) 27/2 years

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If the price of steak is currently $1.00 a pound, and the price triple  [#permalink]

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New post Updated on: 22 Oct 2017, 09:04
Bunuel wrote:
If the price of steak is currently $1.00 a pound, and the price triples every 6 months, how long will it be until the price of steak is $81.00 a pound?

(A) 1 year
(B) 2 years
(C) 5/2 years
(D) 13 years
(E) 27/2 years


1-----6 Months------3------6M-------9------6M--------27------6M------81, so after \(24\) months the price will be $81. Hence time \(=2\) years

Another approach - Use GP formula \(a_n=a_1r^{n-1}\)

here \(a_1=3\), \(a_n=81\) & \(r=3\) and \(n\) is the number of period of 6 months each

so \(81=1*3^{n-1} =>3^4=3*3^{n-1} => n=4\)

Hence time in years \(=2\)

Option B

Originally posted by niks18 on 22 Oct 2017, 08:48.
Last edited by niks18 on 22 Oct 2017, 09:04, edited 3 times in total.
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Re: If the price of steak is currently $1.00 a pound, and the price triple  [#permalink]

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New post 22 Oct 2017, 08:56
Bunuel wrote:
If the price of steak is currently $1.00 a pound, and the price triples every 6 months, how long will it be until the price of steak is $81.00 a pound?

(A) 1 year
(B) 2 years
(C) 5/2 years
(D) 13 years
(E) 27/2 years


Every 6 months, the price of steak triples.

Current price is 1$,
6 months later, the cost become 3$
1 year later, the cost become 9$
1 year 6 months later, the cost becomes 27$
2 years later, the cost become 81$(Option B)

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Re: If the price of steak is currently $1.00 a pound, and the price triple  [#permalink]

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New post 25 Oct 2017, 12:30
Bunuel wrote:
If the price of steak is currently $1.00 a pound, and the price triples every 6 months, how long will it be until the price of steak is $81.00 a pound?

(A) 1 year
(B) 2 years
(C) 5/2 years
(D) 13 years
(E) 27/2 years


Here's one I might make a stupid mistake on as I am prone to this about 5 or 6 times out of 37 questions.

On paper, I sketched out each time period:
0 1 2 3 4
1 3 9 27 81

It takes 4 time periods to get to 81. Each time period is six months, therefore, it takes 24 months, or two years, to compound the steak until $81.

B
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Re: If the price of steak is currently $1.00 a pound, and the price triple &nbs [#permalink] 25 Oct 2017, 12:30
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