I was in the grad program at a top 5 stats program. Cheating was rampant. I discovered this in a 2nd semester grad level math stats course. There were 4 problems on the test, and one of them could only be solved either by being much smarter than me or by getting kind of lucky and very quickly divining the right, tricky way to factor the product of some characteristic functions. I thought it was very non obvious. When the class discussed the test there was a bimodal distn of scores on that question; 3 students, including me, got 1/2 credit and everyone else got 0 or full credit. I asked a classmate how in the hell he figured out the problem in the very tight time limit for the test. He basically told me that last year's test -- not distributed by the professor -- had almost an identical problem on it. Once you'd seen the right way to factor the characteristic function the problem was trivial. Pretty disappointing.