Certain questions

Mainhoon,

I've never actually seen a GMAT question that hinged on your ability to choose between "may" or "might." That said, "might" has to do with something that is uncertain: "The Yankees might lose the game tonight."

In contrast, "may" could have to do with permission.

For example: "May I ask a question?" --> you say "may" because you're not sure the person to whom you are asking the question will grant you permission to do so. (Incidentally, if you say: "Can I ask you a question?" you are questioning your physical ability to ask the question.)
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When you have a modifier that starts with a ", which", it must refer to the single word before the comma:

"I've spent the last ten years building my house, which is blue." --> The modifier "which is blue" refers to the word "house."

The only real exception here is if you have a subject such as:

"Work of art" or "house of magic."

With these, the modifier beginning with the ",which" would refer to the "work" and the "house." These constructions are allowed because the "of art" and "of magic" phrases are necessary components of the "work" and the "house."

Good luck!