What is the largest integer $n$ for which $3\left(n^{2007}\right)<3^{4015}$ ?
(A) 2
(B) 3
(C) 6
(D) 8
(E) 9

## Part C: Each correct answer is worth 8.
Since $3\left(n^{2007}\right)<3^{4015}$, then $n^{2007}<\frac{3^{4015}}{3}=3^{4014}$.

But $3^{4014}=\left(3^{2}\right)^{2007}=9^{2007}$ so we have $n^{2007}<9^{2007}$.

Therefore, $n<9$ and so the largest integer $n$ that works is $n=8$.

ANSWER: (D)