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

Question

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

Are You Up For the Challenge: 700 Level Questions

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

Are You Up For the Challenge: 700 Level Questions

CareerGeek · Answer

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

Archit3110 · Answer

total plums in 3rd year = 50
4th year = 50-3 ; 47
5th year = 47-4 ; 43
6th year = 43-5 ; 38
IMO C ; 38

Kinshook · Answer

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

fireagablast · Answer

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?

CrackverbalGMAT · Answer

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!

Avysar · Answer

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

Posted from my mobile device

Sef237 · Answer

Hello,
Is the question clear enough? i mean, the question says rounded to the nearest integer. 
during the 6th year, if i'm between January to June the number of plums during 6th year = number of plums during 5th year - 5, but i i'm between June to December, the number of plums during 6th year = number of plums during 5th year - 6. What makes you guys decide between both?

XLmafia21 · Answer

the language of question stem is ambiguous . I considered the age for the current year and not the previous year or am i missing something here?  Bunuel

Faszbendarr · Answer

Hey,  Kinshook

I understand the concept for 2nd year but could you please elaborate a little on why are we adding x - (1+2) instead of x - 2 for 3rd year and x - (1+2+3) instead of x -3 for 4th year and so on?

Bunuel · Answer

Ambiguous wording. Archiving the topic.

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

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