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

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16 Apr 2012, 21:41

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45% (01:37) correct
55% (02:06) wrong based on 613 sessions

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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? (A) the average number of oak tree 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.

Let L = the number of leaves on the leafiest tree.

The number of trees must be at least L + 1.

The range of possible numbers of leaves for each tree is from 1 up to L.

If there are L + 1 trees with the number of leaves ranging from 1 to L, there must be at least two trees with the same number of leaves.

E.g. if the tree with the most number of leaves is 2, there must be at least 3 trees with either 1 or 2 leaves - at least two will have the same number of leaves.

The same applies no matter how many leaves (e.g. if the tree with the most leaves has 10,000 leaves, there are at least 10,001 trees with up to 10,000 leaves - at least two must have the same number).

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

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22 Jun 2012, 08:34

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Chose C. More math than verbal. Since the average number of leaves per oak tree is less than the number of oak trees, at least two oak trees should have the same number of leaves.

In an inference question , you have to stick very close to the premises.

Here the answer is (C) let's say there is an one oak tree in Oregon which has one leaf . Then there must be at least one more oak tree because the no of oak trees in oregon exceed the number of leaves in one oak tree . This second oak tree must have at least one leaf based on the premises ( it may have more than one leaf but it should have at least one leaf) . This you must have at least two oak trees

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

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22 Jun 2012, 17:51

IMO C. Keywords-"atleast" When a question ask about maximum and minimum, verify the extremes, none of the answer talks about the extremes except D&E,in which D deals with the ambiguous numbers and E with other trees so are irrelevant . I agree with "OldFritz" for his reasoning.
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Re: If there are more oak trees in Oregon than there are leaves [#permalink]

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25 Jan 2015, 08:02

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

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06 Mar 2015, 15:31

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Draw it! It is easier like this!

So starting with the number of trees (I chose 4 trees), we add one leaf on each (each should have at least one leaf) and we add extra leaves to all of them, keeping the leaves on each tree fewer than 4 (# of leaves on each tree fewer than the # of trees). Then taking the answer choices on by one we see that C fits.

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

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01 May 2015, 05:58

gmihir 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? (A) the average number of oak tree 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.

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