I'm not really sure what qualifying exams are.
At least when I went to grad school, there were two major sets of exams. The first set was a set of qualifying exams, which were subject area exams in Organic Chemistry, Inorganic Chemistry, Physical Chemistry, Analytical Chemistry, and Biochemistry. You had to qualify in at least four areas, either by passing the qualifying exams or by passing the 500-level introductory course in the area (with a B or better) to continue past the first year of grad school. Very few people passed more than one of the qualifying exams on entry, and most people didn't pass any in my class (about 50 people). Almost everybody was able to qualify by coursework.
The second set of exams were the cumulative exams, given after you had completed all the graduate level coursework required for your program - usually after the second or third year of grad school. These were much more difficult exams, and you had to pass them to continue on to your PhD. If you didn't pass them, you wrapped up your research, wrote your thesis, and got out with an MS.