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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
[Reveal] Spoiler: OA

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If the price of steak is currently $1.00 a pound, and the price triple [#permalink] ### Show Tags 22 Oct 2017, 08:48 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

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] ### Show Tags 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] ### Show Tags 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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