OG 12 <number list>

Okay, so A isn't sufficient. Now, here's why B is sufficient.

Let us go about constructing such a set. Now, let the first element of the set be x, and the second element be y (where x and y could or couldn't be equal). Now, all the other elements absolutely have to be 12 - x - y, since the sum of the first and second element with any of the other elements has to be 12. Now, by the same argument, the third, fourth, and fifth elements all have to sum to 12. Because of this,

3 * (12 - x - y) = 12, so 12 - x - y = 4, so x + y = 8.

So, the sum of the first two elements is 8. Now, the sum of the first three elements is 12, so the third element is thus 4. But there's nothing special about the third element... we can let x be the tenth element and y be the eleventh element and repeat the above. By this procedure, we get all the elements to equal 4.

Therefore, the answer has to be B.