# 2002 AMC 12B Problems/Problem 10

## Problem

How many different integers can be expressed as the sum of three distinct members of the set $\{1,4,7,10,13,16,19\}$? $\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 24 \qquad\mathrm{(D)}\ 30 \qquad\mathrm{(E)}\ 35$

## Solution

We can make all multiples of three between 1+4+7=12 and 13+16+19=48, inclusive. There are $\frac{48}{3}-\frac{12}{3}+1=13\Rightarrow \boxed{\mathrm{(A)}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.) integers we can form.