If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 2m + n?
Select the correct option:
A) 11	B) 18	C) 20	D) 25	E) 35

Rationale: k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 2 * 10 + 15 = 35 answer : e
Answer: E