2005 AMC 10A Problem 13

How many positive integers n satisfy the following condition:

\left(130n\right)^{50} > n^{100} > 2^{200} \ \text{?}

\textbf{(A) } 0\qquad \textbf{(B) } 7\qquad \textbf{(C) } 12\qquad \textbf{(D) } 65\qquad \textbf{(E) } 125

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.