OK it's been a little while since I've done AMET but this is what I remember.
There are a number of things to note in this question.
An aircraft is experiencing strong westerly winds while tracking 180 degrees at FL370 over continental australia. The TAT is increasing.
So break the question down. You're up high with a strong westerly, so chances are you are in a JetStream (not associated with a front), more than likely the sub-tropical jetstream.
Where will you find a jetstream? Running perpendicular along the tropopause and stratosphere / upper troposhpere. What does temperature do when you're in the tropopause, stratosphere and troposphere?
What do these do when you are tracking North and what do they do when you're tracking South?
i.e. If I fly in a straight line at the same level to the South, will the jetstream be tropopause be at higher or lower level, thus increasing or decreasing the likelihood of encountering CAT.
Know these things and you'll nail those questions, I had a number of those during my exam.