The data 3, 5, 7, 7, 9, 9, 9, 11 is to be changed by writing in some extra 7s and nothing else. What is the least number of extra 7s needed to make 7 the ONLY mode?

At present 9 appears three times and 7 twice, so 9 is the mode. To make 7 the only mode it must appear MORE often than 9, that is at least four times, which needs 2 extra 7s. Adding just 1 raises 7 to three appearances and ties it with 9, leaving the data with two modes rather than one — a tie is not a sole mode. Adding 3 or 4 would certainly work but the question asks for the least number, and 4 is simply the count 7 has to reach, not the number that must be written in.