2006 AMC 10A Problem 9

Question

How many sets of two or more consecutive positive integers have a sum of

15?

1

2

3

4

5

The sum of

n

consecutive integers is

n

times the middle value

Check

n = 2, 3, 4, 5

The sum of

n

consecutive integers equals

n

times their median. For a sum of

15

:

n = 2

gives

7 + 8,

n = 3

gives

4 + 5 + 6,

and

n = 5

gives

1 + 2 + 3 + 4 + 5.

No set of

4

works (their sum is even), and

6

or more consecutive positive integers already exceed

15.

There are

3

such sets.

Thus, the correct answer is C.

Problem 9 in other years