hardworker, C cannot be a perfect sq.
Yes, I think we are saying the same. The question also askes for an EXCEPT choice - "which of the following cannot be the possible values for A and B".
2. And yes, I agree that the Q is wrongly worked.
The theory that was supposed to be tested is, "12 is already a part of 12AB. To make 12AB perfect square, AB should surely include another 12 (to make it square), among other factors which should be square themselves."
All other choices have a 4 and 3 n AB, making up for the 12 to be square. Only C lacks a 4, and is hence odd man out.
As I have seen before, if the question is wrongly worded/worked out, we can discuss and reject convincingly in forums. But on the real test, if such a problem pops up, we have to choose an answer to move on. In that case, it can be C, the odd man out. After all, all we care for is marks