AMC 10B 2015 Problem 23

Let n be a positive integer greater than 4 such that the decimal representation of n ! ends in k zeros and the decimal representation of (2 n) ! ends in 3 k zeros. Let s denote the sum of the four least possible values of n. What is the sum of the digits of s ?

Answer Choices
A. 7
B. 8
C. 9
D. 10
E. 11