If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest value of n?
Answers:
A) 1 B) 2 C) 3 D) 4 E) 5

Rationale: = 10 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 5 ! − 2 ∗ 5 ! ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 = 5 ! ∗ 10 ∗ 3 ∗ 8 ( 125 ) = 5 ∗ ( 2 ∗ 2 ) ∗ 3 ∗ 2 ∗ ( 5 ∗ 2 ) ∗ 24 ∗ 5 ∗ 5 ∗ 5 = 5 ∗ 2 ∗ 5 ∗ 2 ∗ 5 ∗ 2 ∗ 5 ∗ 2 ∗ 24 ∗ 5 ∗ 3 = 10 ^ 4 ∗ 2 ^ 4 ∗ 5 ∗ 3 = 10 ^ 4 ∗ 5 ∗ 2 ∗ 12 ∗ 3 = 10 ^ 5 ∗ 36 answer : e
Answer: E