Question 134
Consider the following operation. Given a positive integer $n$, if $n$ is a multiple of $3$, then you replace $n$ by $\frac{n}{3}$. If $n$ is not a multiple of $3$, then you replace $n$ by $n+10$. Then continue this process. For example, beginning with $n=4$, this procedure gives $4 \rightarrow 14 \rightarrow 24 \rightarrow 8 \rightarrow 18 \rightarrow 6 \rightarrow 2 \rightarrow 12 \rightarrow \dots$. Suppose you start with $n=100$. What value results if you perform this operation exactly $100$ times?
(A) 10 (B) 20 (C) 30 (D) 40 (E) 50
(A) 10 (B) 20 (C) 30 (D) 40 (E) 50