I've done this exercise focusing on phrasal verbs. There was a sentence, something like this:
I need to ...... it over before I make my decision.
The particle "over" gave me only two choices - mull x think, whose respective definitions are:
mull over - to think carefully about something over a period of time
think over - to consider a problem or decision carefully
The key says that the only correct answer is "think over" (at school I was prudently told that even though a textbook can be the best ever, it does not mean the key is always correct (which is an assumption that has been confirmed by this very key, in which I have already found two mistakes).
Both these words seem identical with little to no difference in their meanings. Can, possibly, native speakers see that big a difference between them that would limit their interchangeability? If you go to a car dealership and the person there tells you:
"Here´s the complete catalogue, go home and think/mull it over."
According to their definitions, both words seem perfectly correct.