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16 Apr 2012, 21:41
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (02:06) correct
59%
(02:22)
wrong
based on 980
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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.
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.
16 Apr 2012, 22:15
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Answer is C:
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).
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).
General Discussion
boomtangboy
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16 Apr 2012, 23:07
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Good Questions !!!
Highly Wordy
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Highly Wordy
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