1998 CEMC Pascal Problems/Problem 8

Problem

The average (mean) of a list of $10$ numbers is $0$ . If $72$ and $-12$ are added to the list, the new average will be

$\text{ (A) }\ 30 \qquad\text{ (B) }\ 6 \qquad\text{ (C) }\ 0 \qquad\text{ (D) }\ 60 \qquad\text{ (E) }\ 5$

Solution

We can just add $72$ and $-12$ to whatever the sum of the original $10$ numbers were, and then divide it by the new number of numbers, which is $12$ .

Let $s$ be the sum of the numbers before $72$ and $-12$ were added. We can then set up an equation involving $s$ to find the average:

$\frac{s}{10} = 0$

$s = 0 \times 10 = 0$

Our new average would then be $\frac{s + 72 - 12}{12} = \frac{0 + 60}{12} = \frac{60}{12} = \boxed {\textbf{(E) } 5}$

~anabel.disher

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1998 CEMC Pascal Problems/Problem 8

Problem

Solution