tyrosine is polar. in theory, it should be exterior. IMO, this type of "not clear cut" question won't be on the MCAT. That's one of the downfall of some test companies. AAMC will give you a more clear cut one. They want you to understand the concept not the detail. Who can remember everything?
This question is wrong in my opinion. You aren't taught HOW polar an amino acid is in biochemistry. You are taught that certain AAs are polar and certain are non-polar, etc. Stack that on with your internal knowledge of biology and you have your answer. I chose the same answer as you did when I took that test. Pissed me off.