In addition to the excellent posts above, here is some food for thought:
Note the wording of the question: "A fair die is rolled once and a fair coin is flipped once. What is the probability that
either the die will land on 3
or that the coin will land on heads?"
Especially "
either the die will land on 3
or that the coin will land on heads"
=> .
....either 3 OR heads
=> 1/6 + 1/2 - 1/6*1/2 - 1/6*1/2 =[spoiler]
6/12 = 1/2[/spoiler]
Here we subtract (1/6)*(1/2)
twice to avoid counting the both "3 and heads" condition
This solution excludes the "3 AND Heads" condition altogether because of the "either 3... OR heads" in the question.
IF the question had been worded thus: "A fair die is rolled once and a fair coin is flipped once. What is the probability that either ('any' would be even better) of these events happen: the die will land on 3 or that the coin will land on heads?"
OR something like
"A fair die is rolled once and a fair coin is flipped once. What is the probability that, at least, the die will land on 3 or that the coin will land on heads?"
Or something else which removes the "either 3... OR heads"
Then the solution would be 1/2 + 1/6 - (1/6)*(1/2) = 7/12
Here we subtract (1/6)*(1/2) only once to avoid a double count of both "3 and heads" condition
So IMO if the OA is 7/12, then either the question or the answer needs to be edited.
As is, with the "either 3... OR heads", The answer Pr = 1/2 is more justifiable, though one could argue for 7/12 with some GMAT specific esotericism.
Hope this adds some value to an already interesting discussion 
