In a set of five numbers, the average of two of the numbers is 12 and the average of the other three numbers is 7 . The average of all five numbers is
(A) $8 \frac{1}{3}$
(B) $8 \frac{1}{2}$
(C) 9
(D) $8 \frac{3}{4}$
(E) $9 \frac{1}{2}$

1957
In a set of five numbers, the average of two of the numbers is 12 and the average of the other three numbers is 7 . The average of all five numbers is
(A) $8 \frac{1}{3}$
(B) $8 \frac{1}{2}$
(C) 9
(D) $8 \frac{3}{4}$
(E) $9 \frac{1}{2}$

## Solution

In order that two numbers have an average of 12, the sum of the two numbers must have been 24.

Similarly, the three numbers must have had a sum of 21 .

Thus the average of the five numbers is, $\frac{21+24}{5}=9$.

ANSWER: (C)