1962 AHSME Problems/Problem 8

Problem

Given the set of $n$ numbers; $n > 1$ , of which one is $1 - \frac {1}{n}$ and all the others are $1$ . The arithmetic mean of the $n$ numbers is:

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ n-\frac{1}{n}\qquad\textbf{(C)}\ n-\frac{1}{n^2}\qquad\textbf{(D)}\ 1-\frac{1}{n^2}\qquad\textbf{(E)}\ 1-\frac{1}{n}-\frac{1}{n^2}$

Solution

Just take $\frac{1(n-1)+(1-\frac{1}{n})}{n}$ . You get $\frac{n-1+1-\frac{1}{n}}{n}$ , which is just $\frac{n-\frac{1}{n}}{n}$ , which is just $\boxed{D}$

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1962 AHSME Problems/Problem 8

Problem

Solution