1959 AHSME Problems/Problem 13

Problem

The arithmetic mean (average) of a set of $50$ numbers is $38$. If two numbers, namely, $45$ and $55$, are discarded, the mean of the remaining set of numbers is: $\textbf{(A)}\ 36.5 \qquad\textbf{(B)}\ 37\qquad\textbf{(C)}\ 37.2\qquad\textbf{(D)}\ 37.5\qquad\textbf{(E)}\ 37.52$

Solution

Since the arithmetic mean of the $50$ numbers is $38$, their sum must be $50*38 = 1900$. After $45$ and $55$ are discarded, the sum decreases by $45 + 55 = 100$, so it must become $1900 - 100 = 1800$. But this means that the new mean of the remaining $50 - 2 = 48$ numbers must be $\frac{1800}{48} = 37.5$. Thusly, our answer is $\boxed{\textbf{(D)}}$, and we are done.

See also

1959 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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