3 integers: x, y, z if there is a multiple of 7?
1: x + y + z is a multiple of 7
2: xyz is a multiple of 7
1: x + y + z is a multiple of 7
2: xyz is a multiple of 7
S1::x, y, and z are all integers. Is at least one of them a multiple of 7?
x + y + z = 7 * some integer
We could have 1 + 2 + 4, or we could have 7 + 14 + 21; NOT SUFFICIENT.
S2::
xyz = 7 * some integer
Since each side consists entirely of integers, each side must have the same prime factorization. Since 7 appears in the prime factorization of the right side, it must also appear in the prime factorization of the left side. That means that at least one of x, y, and z contains a factor of 7 in its prime factorization, so one of them must divide by 7.
