The difficulty here is the word.co-prime

Not everyone accepts this convention, "The numbers 1 and −1 are coprime to every integer, and they are the only integers to be coprime with 0." See this page.

Thus any triple that contains at least one zero has the given property.

There are of those.

But so does the triple , as does (there are three of those).

The triple also (three of them).

Now I have no idea why it would ask "What is the value of a+b?"

For many reasons, I think this is a flawed question.