The interviewer asks you, "Have you ever had to deal with two great people on your team who just didn't get along?" Or, "Have you ever had an unexpected hit to your budget?" 

If you've gotten questions like this, the temptation is to say "Yes, I once had two strong performers who couldn't get along, I understand!" You answered the question, right?

That answer would not be enough today. Why? Without saying so, the interviewer also very much wants to know how you solved that problem. What result did you get that took care of it?

Interviewers are harried and preoccupied. Candidates need to connect the dots between the employer's needs AND their own successes. An answer that implies you can handle the situation is not nearly as strong an answer as one that clearly shows you can do so because you have done well before.

That's what you have to tell them: "Yes, I had Sandy and Kim, each very accomplished but who instantly disliked one another. I met with each of them, separately, and then together, pointing out how each of them was critical to the projects ahead, especially if they teamed together. After we discussed all the opportunities their teamwork would give them, tension was way less, and they actually went on to be the company's 'dynamic duo'. It was a happy ending that the problem was solved."

So point out how you solved the problem they ask you about, with that final part of the story, and you'll be the strongest candidate.