Statement 1
We know that 200 students are taking undergraduate courses. We know that since there are 250 students in total, at least 50 students must be taking only graduate courses. However, we don't know how many of these 200 students taking undergraduate courses are taking only undergraduate classes and how many are taking both undergraduate and graduate classes. So any number of these 200 students could also be taking graduate classes, but we just don't know. Insufficient.
Statement 2
We know 50 students are taking both undergraduate and graduate classes. But what kinds of classes are the other 200 students taking? Are all 200 only undergraduate? Are all 200 only graduate? Are half only undergraduate and half only graduate? We don't know again. Insufficient.
BOTH
If 200 students are taking undergraduate courses, and 50 students are taking both undergraduate and graduate courses, 150 students must be taking only undergraduate classes. If there are 250 students in total, this means that 50 students are taking only graduate classes. So there are 50 students taking only graduate classes and 50 students taking both undergraduate and graduate courses, there are 100 students total taking graduate courses. Sufficient.
I highly recommend making some kind of visual representation for this kind of problem to keep track of information - let me know if you want more info on how to do this!
