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head scratching!!

by mehaksal » Wed Aug 15, 2012 6:10 am
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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by mehaksal » Wed Aug 15, 2012 6:12 am
do such questions actually appear in the actual exam?!!
meanwhile, here is it A or C??
smbdy explained C to be the answr using the method of induction!! blew over my head!!
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by techyrajeev » Wed Aug 15, 2012 6:50 am
C can be the answer. If we take the boundary example:there are four oak trees with 1,2,3 and some leaves tree. last tree must have number of leaves equal to any of the remaining trees otherwise argument conditions will not be met.
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by crisro » Wed Aug 15, 2012 2:52 pm
IMO C is the answer. My reasoning is that if we have a single tree with one leaf and there are more trees than there are leaves on one tree, we must have the second tree with one leaf. If we have only two trees, one with one leaf and the second with two leaves, then we must have the third tree with either one or two leaves; and we can continue with the same reasoning.
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by hjafferi » Wed Aug 22, 2012 6:15 am
Stumped....:(
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by KapTeacherEli » Wed Aug 22, 2012 11:55 am
Though you do not need to have this memorized, it's actually an important mathematical rule called the pigeonhole principle. It is rarely tested, but it can show up. For instance, one Kaplan practice question reads, "If there are 10 white sox, 8 black socks, and 12 blue socks in a drawer, what is the smallest number of socks that can be selected at random that guarantees a pair of the same color is selected?"

[spoiler]Well, here, the "pigeonholes" are the colors. Three socks could be one of each color. But once we have four, we have more socks than colors, and therefore at least once color has to have two socks.[/spoiler]
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by mohan514 » Fri Aug 24, 2012 9:56 pm
KapTeacherEli wrote:Though you do not need to have this memorized, it's actually an important mathematical rule called the pigeonhole principle. It is rarely tested, but it can show up. For instance, one Kaplan practice question reads, "If there are 10 white sox, 8 black socks, and 12 blue socks in a drawer, what is the smallest number of socks that can be selected at random that guarantees a pair of the same color is selected?"

[spoiler]Well, here, the "pigeonholes" are the colors. Three socks could be one of each color. But once we have four, we have more socks than colors, and therefore at least once color has to have two socks.[/spoiler]
it is still not clear sir

can you pleas elaborate your concept

never heard of this thing..
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by KapTeacherEli » Mon Aug 27, 2012 7:53 pm
Hi mohan,

Check out the link to the wikipedia article in my last post, then let me know if you have questions--though as I said, this is pretty uncommonly tested!

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by ankit0411 » Tue Aug 28, 2012 11:21 pm
mehaksal 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.
I came down to C.

Below is what I think might be possible :

1 tree - 5 leaves

# of trees - 6

So total leaves (max) 6*5= 30

Hence, in this case each tree has 5 leaves.

Now if the number of leaves in each tree is different, but remember max # of leaves can by 5 only.

5 4 3 2 1 ( this no can again be either 1,2,3,4 or 5 )

Hence 2 trees will have the same no of leaves.

Hope I understood this right.

Thanks,
Ankit
Don't predict future , create it !
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