1999 CEMC Gauss (Grade 7) Problems/Problem 8

Problem

The average of $10$ , $4$ , $8$ , $7$ , and $6$ is

$\text{(A)}\ 33 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 7$

Solution 1

The sum of all the listed numbers is

$10 + 4 + 8 + 7 + 6 = 35$

Since there are five numbers, we can divide the sum by $5$ to get the average:

$\frac{35}{5} = \boxed {\textbf {(E)} 7}$

Solution 2 (answer choices)

$10$ is too large of an answer because the largest number listed is $10$ but there are numbers that are less than $10$ , so the average will be lower than $10$ .

The only answer choice that is less than $10$ is $\boxed {\textbf {(E)} 7}$ .

Solution 3

From the list of numbers, we can observe that the numbers are all centered around 7. $8$ and $6$ are both $1$ away from $7$ , and $4$ and $10$ are both $3$ away from $7$ . $7$ is equal to itself.

Thus, the answer is $\boxed {\textbf {(E)} 7}$ .

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1999 CEMC Gauss (Grade 7) Problems/Problem 8

Contents

Problem

Solution 1

Solution 2 (answer choices)

Solution 3