2002 AMC 12B Problem 10

How many different integers can be expressed as the sum of three distinct members of the set

\{1,4,7,10,13,16,19\}?

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Solution

Every element is one more than a multiple of

3,

so any sum of three of them is a multiple of

3.

The smallest sum is

1+4+7=12

and the largest is

13+16+19=48,

and every multiple of

3

between them is attainable. There are

13

multiples of

3

from

12

48.

Thus, the correct answer is A.

Tagged: modular arithmetic · counting integers in a range