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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 [#permalink]

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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?

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

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

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

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

there must be more oak trees than any other type of tree in Oregon
[Reveal] Spoiler: OA

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Re: oak trees [#permalink]

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New post 19 Dec 2010, 23:08
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".

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Re: If there are more oak trees in Oregon than there are leaves [#permalink]

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New post 28 May 2013, 08:35
Iam Not Getting this Problem-Can anyone Help! :roll:

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Re: If there are more oak trees in Oregon than there are leaves [#permalink]

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New post 28 May 2013, 12:00
shrive555 wrote:
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?

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

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

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

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

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


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
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Re: If there are more oak trees in Oregon than there are leaves [#permalink]

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New post 15 Aug 2016, 22:22
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Re: If there are more oak trees in Oregon than there are leaves [#permalink]

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New post 16 Aug 2016, 05:54
KyleWiddison wrote:
shrive555 wrote:
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?

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

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

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

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

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








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




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?

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Re: If there are more oak trees in Oregon than there are leaves [#permalink]

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New post 16 Aug 2016, 12:10
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.

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Re: If there are more oak trees in Oregon than there are leaves   [#permalink] 16 Aug 2016, 12:10
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