There are a numbers in A, The median is 85, the average

Question

There are a numbers in A, The median is 85, the average value is 82. There are b numbers in B, the median is 78, the average value is 75. Is the median number greater than the average value, after A and B are mixed.
(1) a+b=97
(2) a=42,b=37

Please suggest structured and quick approach to such problems.
OA later.

KillerSquirrel · Answer

In this kind of problems, the answer usually (E). we can't tradeoff median and average even when it looks we can. I would be very surprised if the answer is differ then (E). furthermore (and i think its just a mistype) the data in statement 1 & statement 2 contradict since 97 <> 79. :-D

KillerSquirrel · Answer

vshaunak@gmail.com , what's the OA ? Thanks

LM · Answer

A : (Sum/a) = 82 => Sum = 82*a and Median is 85

B : (Sum/b) = 75 => Sum = 75*a and Median is 78

from(1)
(A+B) : (Sum/(a+b)) =   / (a +b) = 5*(17*a + 15*b)/(a+b) = 5*(17*a + 15*b)/(97)

We don't know average and have no clue about the median, thus insufficient

from(2)
(A+B) : (Sum/(a+b)) =   / (a +b) = 5*(17*a + 15*b)/(a+b) = 5*(17*42 + 15*37)/(79) = 80.32

We know the average but have no clue about the median, thus insufficient

The answer is E.

and I will agree with squirrel that " In this kind of problems, the answer usually (E). we can't tradeoff median and average even when it looks we can. I would be very surprised if the answer is differ then (E). "

vshaunak@gmail.com · Answer

Thanks guys OA is 'E'.

Caas · Answer

Hey KillerSquirrel and All!

How do you think if I change this DS problem as follows, whould it have answer (A)?


There are a numbers in A, The median is 85, the average value is 82. There are b numbers in B, the median is 78, the average value is 75. Is the median number greater than the average value, after A and B are mixed. 
 (1) a=b 
(2) a=42,b=37 

My reasoning: There is a rule that if we combine 2 data sets, the average of the resulting set is the average of the averages of the 2 original sets.
So we can say that the average of the mixed set will be (82+75)/2=78,5
Half of the question is answered.
But what about median????

There are a numbers in A, The median is 85, the average

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