Hey All,
I got asked about this by PM (but don't PM me anymore, because I'm tying up all my forum loose ends and then taking a break). So here I am. Quickly:
a) as above
CORRECT: Yes, "at the urging of" is a common idiomatic usage.
b) as a consequence of having been urged by his own doctor, his advisers, and a coalition of some
PROBLEM: "A consequence" is illogical. It's not as if there were multiple consequences of the urging. The ONLY consequence was that he did it.
c) on account of being urged by his own doctor, chief advisers, and a coalition of
PROBLEM: Never pick answer choices with "being" unless you see three or more answer choices with "being" in them. It's a horrible way to construct a sentence, and GMAC pretty much always makes it wrong.
d) as he was urged to do by his own doctor, his chief advisers, and a coalition of some
PROBLEM: "As" can be unclear, because it can have the meaning we expect here ("As expected, he took the bait."), OR be related to time ("As he opened the door, he realized he was in the wrong apartment."). It's unclear which this one is.
e) as his own doctor was urgning him to do, along with his chief advisers, and a coalition of
PROBLEM: Same as D, also the parallelism is messy, because the "along with" is unnecessary.
Hope that helps!
-t