1955 AHSME Problems/Problem 3

Problem

If each number in a set of ten numbers is increased by $20$ , the arithmetic mean (average) of the ten numbers:

$\textbf{(A)}\ \text{remains the same}\qquad\textbf{(B)}\ \text{is increased by 20}\qquad\textbf{(C)}\ \text{is increased by 200}\\ \textbf{(D)}\ \text{is increased by 10}\qquad\textbf{(E)}\ \text{is increased by 2}$

Solution 1

Let the sum of the 10 numbers be x. The mean is then $\frac{x}{10}$ . Then, since you're adding 20 to each number, the new sum of the numbers is x+200, since there are 10 numbers. Then, the new mean is $\frac{x+200}{10}$ , which simplifies to $\frac{x}{10}+20$ , which is $\fbox{B}$ .

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1955 AHSME Problems/Problem 3

Problem

Solution 1