The average (mean) of a list of $n$ numbers is 7 . When the number -11 is added to the list, the new average is 6 . What is the value of $n$ ?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
The average of a list of numbers is their sum divided by how many numbers are in the list. Thus if $n$ numbers have an average of 7 their sum is $7 n$.

When -11 is added to the list of numbers, there are then $n+1$ numbers whose sum is $7 n-11$. Using this, we obtain

$$
\begin{aligned}
\frac{7 n-11}{n+1} & =6 \\
7 n-11 & =6 n+6 \\
n & =17
\end{aligned}
$$

ANSWER: (E)