"At" the nick of time? Are you kidding? I suppose it makes sense if "The Nick of Time" is a place: They arrived at The Nick of Time - a jail for chrononauts! Obviously the answer is "In" - I just can't believe that over 50% of people think it's "at".
Prepositions are difficult for non native speakers, but to arrive "at the nick of time" would require "nick" to be a specific place and it isn't.
It is nice to do such exercise, it will definitely improve English Language skills thanks