What is the date of your last your last medical exam?

The interviewer should never ask this question but you can choose to play along or you can opt out of the answer tactfully. Asking a question in return is a very smart way to show the interviewer that the question is entirely inappropriate without having to say so in a point-blank manner.

Here are 2 options:

"My health is very important to me and I'm sure to visit my doctor regularly. Why do you ask? Would you like a referral?"

OR

"Oh wow, I have never been asked that question in an interview. How is this relevant to the position?"

Please note: If you are asked this question, you are within your rights to leave the interview and make an official complaint to the company's HR department or to your local labor standards board. Do not worry about blowing the interview. You do not want to work for such an irresponsible organization.