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# Each year for 4 years, a farmer increased the number of trees in a .

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Intern
Joined: 16 May 2017
Posts: 33
Location: India
Each year for 4 years, a farmer increased the number of trees in a .  [#permalink]

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04 Dec 2017, 22:50
OG 2018
Question no - 163

Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard the preceding year. If all of the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period?

A. 1,250
B. 1,563
C. 2,250
D. 2,560
E. 2,752
Intern
Joined: 16 May 2017
Posts: 33
Location: India
Re: Each year for 4 years, a farmer increased the number of trees in a .  [#permalink]

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04 Dec 2017, 23:01
Hi all

I got this question incorrect at the time of timed practice and then I tried to look it up here in the community but could not find. Luckily, i was able to figure the solution through back-calculation so I am posting it. It may help others as it will take hardly 10 seconds to get the answer and i was silly enough not to get this one right.

Solution-

We can get a general formula which is being repeated for the tree growth. i.e. if the no of trees be x last year, the no of trees next year will be
x+x/4 =5x/4

Let's assume that at the end of 3rd year, three population was x.

end of the fourth year =6250
end of the third year ...5x/4= 6250.... x=5000
end of the second year 5x/4=5000.... x=4000
end of the first year 5x/4=4000...... x=3200
start of tree plantation -5x/4=3200... x=2560

thnaks
subhankar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6499
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Each year for 4 years, a farmer increased the number of trees in a .  [#permalink]

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07 Dec 2017, 22:19
1
bapism07 wrote:
Hi all

I got this question incorrect at the time of timed practice and then I tried to look it up here in the community but could not find. Luckily, i was able to figure the solution through back-calculation so I am posting it. It may help others as it will take hardly 10 seconds to get the answer and i was silly enough not to get this one right.

Solution-

We can get a general formula which is being repeated for the tree growth. i.e. if the no of trees be x last year, the no of trees next year will be
x+x/4 =5x/4

Let's assume that at the end of 3rd year, three population was x.

end of the fourth year =6250
end of the third year ...5x/4= 6250.... x=5000
end of the second year 5x/4=5000.... x=4000
end of the first year 5x/4=4000...... x=3200
start of tree plantation -5x/4=3200... x=2560

thnaks
subhankar

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Re: Each year for 4 years, a farmer increased the number of trees in a . &nbs [#permalink] 07 Dec 2017, 22:19
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# Each year for 4 years, a farmer increased the number of trees in a .

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