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# Each year for 4 years, a farmer increased the number of tree

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Manager
Joined: 14 May 2015
Posts: 54

Kudos [?]: 6 [0], given: 2

Re: Each year for 4 years, a farmer increased the number of tree [#permalink]

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09 May 2017, 21:39
x(1.25)^4 = 6250
x=2560
ans:D

Kudos [?]: 6 [0], given: 2

Intern
Joined: 24 May 2016
Posts: 19

Kudos [?]: 7 [1], given: 163

Location: Germany
Each year for 4 years, a farmer increased the number of tree [#permalink]

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04 Jun 2017, 02:26
1
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Another approach would be test the answers:
Normally, starting with B or D, I have chosen D as it is a cleaner number.
Assuming the farmer had at the beginning 2,560 trees he will have one year later (2,560 *1,25) or calculate 1/4 of it and add it.
--> After 1 year: 3200 trees
--> 2. Year: 3200*1,25= 4000 trees
--> 3. Year: 4000*1,25= 5000 trees
--> 4. Year: 5000*1,25= 6250 trees - Bingo!
As we arrived to the desired value Answer D is correct! The hint was that after the first year the numbers cleaned up very nicely and the calculations involved less work.

Kudos [?]: 7 [1], given: 163

Manager
Joined: 23 May 2017
Posts: 157

Kudos [?]: 52 [0], given: 7

Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: Each year for 4 years, a farmer increased the number of tree [#permalink]

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10 Jul 2017, 23:25
IMHO I think we can skip the calculation part in this question.

my reasoning behind solving this question was : since the number of trees are increasing in a fashion of 1/4 .
so by end of 4th year we will have a number which is of form X/64....( we are adding 1/4 three times in the initial number) Total number of trees in the orchard after 4 years = 6250, factor of which does not have 64 : so we must have a initial number which will have a factor of 64 or we can say the number must be divisible by 64.

Let's scan the numbers : let's start finding the number which is divisible by 8

A. 1250
B. 1563
C. 2250
D. 2560 --> divisible by 8
E. 2752 --> divisible by 8

so we have only two options to check for further divisibility: as we further divide the number by another 8 we will see only D fits our requirement
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Kudos [?]: 52 [0], given: 7

Intern
Joined: 17 Oct 2014
Posts: 5

Kudos [?]: 1 [0], given: 25

Re: Each year for 4 years, a farmer increased the number of tree [#permalink]

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25 Aug 2017, 00:32
imhimanshu wrote:
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 of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752

Can someone walk me through the logic behind this question. I am able to solve this by using options as well as by assuming the number of trees = x. However, had the question been, "If all of the trees thrived and there were 6250 trees in the orchard at the end of 15 year period, how many trees were in the orchard at the beginning of the 4 year period". then it would have been difficult to solve.

Thanks

I have figured out another method to it which is short but I am unaware if it is appropriate:
2560 is the only number in the given option which has factors: 2*5*4^4. Thus being the only number 4^4 directly qualifies.

Please guide if my concept is wrong

Kudos [?]: 1 [0], given: 25

Re: Each year for 4 years, a farmer increased the number of tree   [#permalink] 25 Aug 2017, 00:32

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