CAYLEY 2018 Problem 22

If n is a positive integer, the symbol n ! (read " n factorial") represents the product of the integers from 1 to n. For example, 4!=(1)(2)(3)(4) or 4!=24. If x and y are integers and \frac{30!}{36^{x} 25^{y}} is equal to an integer, what is the maximum possible value of x+y ?

Answer Choices
A. 10
B. 47
C. 17
D. 26
E. 13