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 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.

bobfirth · Accepted Answer

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).

boomtangboy · Answer

Good Questions !!!

Highly Wordy

+1 Kudos

rajcools · Answer

c)

good question and good reply by bobfirth

georgepaul0071987 · Answer

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

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rajeevrks27 · Answer

good one. got confused in the words.

sidhu09 · Answer

A very good question.

Great explanation by  bobfirth

Thank you

narangvaibhav · Answer

Good question and great explanation

saikarthikreddy · Answer

Good question and very nice explanation !!

tuanquang269 · Answer

I got a trap in choice B.

Thank for explanation of bobfirth is exactly what I rethink

OldFritz · Answer

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.

Cheers,
Der alte Fritz

thevenus · Answer

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.

sandyacegmat · Answer

'C' - Good Question!

Took a while to narrow down each choice but interesting Q.

kvazar · Answer

Why is this in CR? It's quant, not CR.

nobita123 · Answer

Very good question!! I was unable to find out the answer at first.

pacifist85 · Answer

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.

ssriva2 · Answer

STARTED WITH NUMBERS-1,2,3

ans-c

johng2016 · Answer

C
What's quantitative CR!

Argument said: the max number of leaves (eg: 100 leaves) < the total trees (eg 110)

==> like the case you divided 5 chicken into 4 cages, it must be one cage with at least 2 chicken

Arro44 · Answer

Are there really questions like this on the actual GMAT? To me this seems more like a wordy quant question...

kmehta80 · Answer

We can consider the number of trees as 10. Since, there are more trees than max leaves on a particular tree and a tree must have atleast 1 leaf. So, we have possible combination

Trees = 10, 
Leaves = Option 1 : 9, 9,9,9,9.... 10 times ==> Average = 9 
Option 2 : 8,8...... 10 times ==> Average = 8
.
.
.
Option 9: 1, 1, .....10 times ===> Average = 1
Also, the number could be 1,2,3,4,5,6,7,8,9, (10th Option) ?? What could be number of leaves 10th tree could have? 
Clearly 10 leaves is not possible as it contradicts the number of trees is MORE than Clause. Hence, it could be either 1 or 2or 3 or4...or 9.

Hence, From all the above options only C works

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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