Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=50, what is the maximum value of y for which f(x,y)=0? Choose the correct choice from the following answers:
A) 35 B) 36 C) 40 D) 42 E) 45

Rationale: the question is finding y such that ( 50 - y ) ! is a multiple of 50 . that means we need to have 2 * 5 ^ 2 in ( 50 - y ) ! 10 ! is the smallest factorial number with 2 * 5 ^ 2 as a factor . 50 - y = 10 y = 40 the answer is c .
Answer: C