"Which category do you fall under? A person who anticipates a problem well, or a person who reacts to a problem well?"
This is a tough question because both options look pretty good. My recommendation would be to answer depending on the position you are applying for. For example, if you are applying for a type of analyst or upper management position, then anticipating a problem would be more useful. However, if you are applying to be a nurse for a hospital emergency room, then reacting to a problem well is stronger.
Short Answers
"I think it's good to be good at both. But in my experience, I realized I react to problems better. Whenever I'm faced with a new problem, I know what steps to take to deal with the problem."
"I believe I'm strong in both, but I try to work more on anticipating problems. In this profession, it's very important to anticipate a problem and fix it before it becomes a real problem."
"I'm very observant and aware of what's going on, so I'm stronger at anticipating problems."
"I'm good at dealing with problems, so I'm a person who reacts to a problem well."
Long Answers
"I feel I react to problems well, but I'm much stronger at anticipating them. I'm a type of person that pays attention to detail, inconsistencies, and subtle signs. Basically, I want to find a potential problem and put measures in place to correct it before it happens. It's interesting to see how the people who deal with problems get rewarded for resolving the issue. What about the people who put the fire out before it even started? So anticipating problems before it happens is what I've always done and I believe it's important in any work environment."
"Being a nurse requires many skills. One of the important traits is to be able to react to problems well. Reacting to a problem well requires the ability for quick thinking, ability to think of all the options available, and maintaining self control in hectic times. In my spare time, I even think about creative problems that might come up. Since a problem can arise at any time and in any form, I try to be as creative as I can and I walk through the situation as if I'm dealing with the problem. So this has helped me to become very good at reacting to problems."
The answer gets stronger with examples, so if you have experienced something that you can explain, feel free to use include it in the answer. Also, if you are unsure about how to say it, remember that you can ask us.