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At a company dinner, each of the 56 employees present ate at least one

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At a company dinner, each of the 56 employees present ate at least one  [#permalink]

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New post 11 May 2018, 11:38
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  55% (hard)

Question Stats:

51% (01:31) correct 49% (01:09) wrong based on 37 sessions

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At a company dinner, each of the 56 employees present ate at least one french toast. What is the median number of french toasts eaten per employee at the dinner?

(1) 16 employees were such who ate less than 3 french toasts each.

(2) 20 employees were such who ate 4 or more french toasts each.



PS:- This question is inspired by the following OG question:

https://gmatclub.com/forum/what-is-the- ... l#p1081764
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Re: At a company dinner, each of the 56 employees present ate at least one  [#permalink]

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New post 11 May 2018, 13:33
amanvermagmat wrote:
At a company dinner, each of the 56 employees present ate at least one french toast. What is the median number of french toasts eaten per employee at the dinner?

(1) 16 employees were such who ate less than 3 french toasts each.

(2) 20 employees were such who ate 4 or more french toasts each.



PS:- This question is inspired by the following OG question:

https://gmatclub.com/forum/what-is-the- ... l#p1081764


We'll try looking for edge cases which contradict the different answer choices.
This is an Alternative approach.

the median number out of 56 employees is the average of the 28th and 29th employee.

(1) If these 16 employees each had 1 toast and all other employees also had 3 toasts, then the median is 1. If all other employees had 4 toasts, the median is 4.
Insufficient.

(2) Similarly to the above, if all employees except these 20 ate 1 toast the median is 1, if all employees except these 20 ate 2 toasts the median is 2.
Insufficient.

Combined:
Since only 16 employees had less than 3 toasts, the median must be at least 3. Can it be 3? Yes - for example if 16 employees had 1 toast, 20 had 4 and all the others had 3.
We'll try to contradict this. Can the median be 4? Since only 20 employees have 4 or more toasts, then the median employees (#28,29) must have less than 4. So the answer must be 3.
Sufficient.

(C) is our answer
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Re: At a company dinner, each of the 56 employees present ate at least one  [#permalink]

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New post 11 May 2018, 15:47
I) we only know have data about people eating less than 3 french toast
But we still don't know how many categories in sample has
It can be divided into various categories
I..e less than 3 or greater than 4 or 5 or 6 and many more so insufficient

II)we got data about more than 4 french toast but don't know whether sample has data about less than 1,2 or 3
So insufficient

Combining both
We have data segregated into 3 categories
I) less than 3=16
II) equal to 3= 56-36=20
III) equal to 4 or greater than 4= 20

So sufficient
Hence C is answer

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Re: At a company dinner, each of the 56 employees present ate at least one &nbs [#permalink] 11 May 2018, 15:47
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