PASCAL 2020 Problem 25

We call the pair ( m, n ) of positive integers a happy pair if the greatest common divisor of m and n is a perfect square. For example, (20,24) is a happy pair because the greatest common divisor of 20 and 24 is 4 . Suppose that k is a positive integer such that (205, 800,35 k) is a happy pair. The number of possible values of k with k \leq 2940 is

Answer Choices
A. 36
B. 28
C. 24
D. 30
E. 27