If there are more oak trees in Oregon than there are leaves

Question

If there are more oak trees in Oregon than there are leaves on any one Oregon oak tree, and if every Oregon oak tree has at least one leaf, then __________.

Which of the following most logically completes the passage?

(A) the average number of oak leaves per Oregon oak tree must be less than half the number of Oregon oak trees

(B) there are fewer leaves on at least one Oregon oak tree than half the number of those trees

(C) there must be at least two oak trees in Oregon with the same number of leaves

(D) there must be at least as many Oregon oak trees with half as many leaves as the Oregon tree with the most leaves, as there are Oregon oak trees with twice as many leaves as the Oregon oak tree with the fewest leaves

(E) there must be more oak trees than any other type of tree in Oregon

anshumishra · Answer

Suppose one of the tree which has maxm number of leaves, has "n" leaves
So, no. of trees = n+1

One of the tree has "n" leaves, the rest will have k leaves ( 1<=k<=n).

So, we have n+1 trees, which can have one of n values :

Clearly at least two of them will have the same number of leaves.

Hence "C".

amitbhar · Answer

Iam Not Getting this Problem-Can anyone Help! :roll:

KyleWiddison · Answer

This is a nice little brain teaser

C is the correct answer due to the constraints of the problem. Because there are more trees than possible numbers of leaves, some of the trees must have the same number of leaves. For example, let's say there are 5 trees, making the possible options for numbers of leaves 1, 2, 3 or 4. Since we have 5 treees and 4 options for number of leaves we have to "share" the same number at least once. The details about leaves and Oregon are distractions from the logical math problem. KW

warriorguy · Answer

Could you explain why D is incorrect? I was unable to wrap my head around its wording.

Also, please help to understand C better? If we have '5' trees , I understand that we have options from 1 to 4. So do we need to apply like optimization rule?

goforgmat · Answer

Basically the argument boils down to

let no of leaves be in descending order as n,n-1,n-2,.....
according to the argument there are atleast n+1 trees
n+1 th tree can have n or n-1 or n-2 etc..
the above expressed in words will be option c.

VerbalBot · Answer

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If there are more oak trees in Oregon than there are leaves

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If there are more oak trees in Oregon than there are leaves

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