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The total number of plums that grow during each year on a certain plum

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The total number of plums that grow during each year on a certain plum  [#permalink]

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New post 01 Nov 2019, 05:22
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The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 3rd year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?

A. 43
B. 41
C. 38
D. 35
E. 32


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Re: The total number of plums that grow during each year on a certain plum  [#permalink]

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New post 05 Apr 2020, 04:12
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fireagablast wrote:
hmm why are we supposed to assume that that year 1 is really year 0, and that we don't start counting the age until the 2nd year?


Hello fireagablast,

I do not think that any of the answers here have considered year 1 as year 0. Nothing has to be subtracted from the number of plums grown in the FIRST year because of the fact that it is the FIRST year.

Only when the tree completes its 365th (or 366th) day of existence will you say that its age is 1 year, right? There’s no concept really like year 0.
We need to subtract 1 from the number of plums grown in the 2nd year, because by then the tree would be a 1 year old ?

Many students get confused with this concept of what happens to the plums grown in the first year. You just don’t subtract anything from it because before the first year, the age of the tree was ZERO (the tree didn’t exist, did it?).

On a lighter note, the argument that the tree existed in a seed is for a different day ?

Hope that helps!
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Re: The total number of plums that grow during each year on a certain plum  [#permalink]

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New post 01 Nov 2019, 05:52
Bunuel wrote:
The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 3rd year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?

A. 43
B. 41
C. 38
D. 35
E. 32


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Let the number of plums during 1st year = n,
during 2nd year = n - 1
during 3rd year = n - 1) - 2 = n - (1 + 2)
during 4th year = (n - (1 + 2)) - 3 = n - (1 + 2 + 3) and so on ...
--> during xth year = n - (1 + 2 + 3 + . . . . . . + (x-1))

Given, n - (1 + 2) = 50
--> n = 53

During 6th year = n - (1 + 2 + 3 + 4 + 5) = n - 15 = 53 - 15 = 38

IMO Option C
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Re: The total number of plums that grow during each year on a certain plum  [#permalink]

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New post 02 Nov 2019, 02:06
1
1
total plums in 3rd year = 50
4th year = 50-3 ; 47
5th year = 47-4 ; 43
6th year = 43-5 ; 38
IMO C ; 38



Bunuel wrote:
The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 3rd year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?

A. 43
B. 41
C. 38
D. 35
E. 32


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Re: The total number of plums that grow during each year on a certain plum  [#permalink]

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New post 28 Mar 2020, 03:21
Bunuel wrote:
The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 3rd year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?

A. 43
B. 41
C. 38
D. 35
E. 32


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Let the Plums grown in 1st year = x
Plums grown in 2nd year = x - (1)
Plums grown in 3rd year = x - (1+2) = 50 ; x = 53
Plums grown in 4th year = x - (1+2+3) = 47
Plums grown in 5th year = x - (1+2+3+4) = 43
Plums grown in 6th year = x - (1+2+3+4+5) = 38

IMO C
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Re: The total number of plums that grow during each year on a certain plum  [#permalink]

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New post 04 Apr 2020, 14:29
hmm why are we supposed to assume that that year 1 is really year 0, and that we don't start counting the age until the 2nd year?
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Re: The total number of plums that grow during each year on a certain plum  [#permalink]

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New post 17 May 2020, 23:41
1
The number of plums that the tree bore during the third year is given to be 50
So during the fourth year the number of plums will be
50- 3 (because during the fourth year, the completed number of years in whole will be 3 ignoring the fractional part)= 47
During the 5th year it would be
47-4=43
During the 6th year it would be
43-5=38
Hence C

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Re: The total number of plums that grow during each year on a certain plum   [#permalink] 17 May 2020, 23:41

The total number of plums that grow during each year on a certain plum

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