1986 AMC 8 Problem 25

Question

Which of the following sets of whole numbers has the largest average?

multiples of

2

between

1

and

101

multiples of

3

between

1

and

101

multiples of

4

between

1

and

101

multiples of

5

between

1

and

101

multiples of

6

between

1

and

101

For evenly spaced numbers, the average equals the average of the smallest and largest

Let

a_1

and

a_n

be the first and last terms; compute

\dfrac{a_1 + a_n}{2}

for each set and compare

For a set of evenly spaced whole numbers, the average is the average of the smallest and largest. The averages are: A:

\dfrac{2 + 100}{2} = 51,

B:

\dfrac{3 + 99}{2} = 51,

C:

\dfrac{4 + 100}{2} = 52,

D:

\dfrac{5 + 100}{2} = 52.5,

E:

\dfrac{6 + 96}{2} = 51.

The largest average is

52.5,

from the multiples of

5.

Thus, the correct answer is D .

Problem 25 in other years