the contestant must answer at least 33 questions correctly in order to end up with over 350 total points. The 100 they start off with means that they should really only have to answer 25 questions correctly, but this is not the case. 33 x 10 = 330, plus the first 100 = 430. This is necessary as a buffer, seeing as how if they get every question other than the necessary 33 wrong, it will be a reduction of 68 points total (17 incorrect, which is minus 4 = 68)
(430 - 68 = 362). I hope this was thoroughly explained and broken down! Best of luck!!