Answer: Option A
:
A be the set of natural numbers less than 100.
$\therefore$ A = {1, 2, 3, 4, ... , 99}
Now, B is the subset of A such that B contains two digit numbers which are divisible by exactly two numbers from the set A .
$\because$ Only prime numbers are the numbers which are divisible by 1 and itself only.
$\therefore$ B = {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
Now, C is the subset of B such that C contains numbers whose sum of digits is divisible by 2.
$\therefore$ C = {11, 13, 17, 19, 31, 37, 53, 59, 71, 73, 79, 97}
Now, D is the subset of C such that D contains numbers whose sum of the digits is a perfect square or a perfect cube.
$\therefore$ D = {13, 17, 31, 53, 71, 79, 97}
$\therefore$ Median of the set D = 53