The mean (average) of five consecutive even numbers is 12 . The mean of the smallest and largest of these numbers is
(A) 12
(B) 10
(C) 14
(D) 8
(E) 16
Solution 1

Consider the set of five consecutive even numbers 8, 10,12,14, 16 .

The mean of these five numbers is $\frac{8+10+12+14+16}{5}=\frac{60}{5}$ or 12 .

If the five consecutive even numbers were smaller, their mean would be less than 12 .

If the five consecutive even numbers were larger, their mean would be greater than 12 .

Therefore, this is the set of five consecutive even numbers that we seek.

The mean of the smallest and largest of these five numbers is $\frac{8+16}{2}=\frac{24}{2}$ or 12 .

Solution 2

The mean of five consecutive even numbers is the middle (third largest) number.

To see this, consider that the smallest of the five numbers is 4 less than the middle number, while the largest of the five numbers is 4 more than the middle number.

Thus, the mean of the smallest and largest numbers is the middle number.

Similarly, the second smallest of the five numbers is 2 less than the middle number, while the fourth largest of the five numbers is 2 more than the middle number.

Thus, the mean of these two numbers is also the middle number.

Since the mean of the five numbers is 12 , then the middle number is 12 .

Therefore, the mean of the largest and smallest of the five numbers is also 12.

ANSWER: (A)