Problem Solving

3� - 1=( 3^4 + 1)( 3^2 + 1)(3+1)(3-1)=82*10*4*2

Median will be equal to mean in this case as the number of terms in the set are even.

Median=Mean= (Sum of all nos)/(No of terms)=82*10*4*2/82=80

Ans =(C)

Immediate inspection tells us that the answer cannot be 41 because it must be even (because the median will lie half-way between 2 odd values). This reduces the problem to 4 possible answers.

The solution below contains a small error, but the principle takes me to the right answer.
If we subtract 1 from each integer, we would get 82 consecutive even numbers with sum Z = (3� - 83)
Half of this would be equivalent to 82 consecutive integers with new sum, S =(3� - 83)/2 = 3239
If our set started with 1 and ended with N, then S would be N(N+1)/2 = 82(82+1)/2 = 3403 > 3239
3403-3239 = 164 = 82*2
So let's try starting with 0 and ending with (N-1): S = 81*82/2 = 3321
So let's try starting with -1 and ending with (N-2): S = 80*81/2 = 3240 (extremely close to 3239)
The median would be the 41.5th value, i.e. 41.5 -2 = 39.5
Double this and add 1 to return to our original set of consecutive ODD numbers: M = 80