The sum of digits of every possible 8 digit number is noted. Which sum occurs most often?

The correct option is D

Both 36, 37

1,00,00,000 and 9,99,99,999 are the first and lat 8 digit number possible. Their sum of digits are 1 and 72 respectively. i.e., all other 8 digit numbers have the sum of their digit lying between 1 and 72.

We seek the most occurring number between 1 and 72. Since there are an even number of (72) sums possible, its median are the 2 middle most values which are 36 and 37.

The distribution of the sums will be symmetric and hence median and mode will coincide. The most occurring sum will be, therefore, both 36, 37.