In order to perform well on a math test you don't always have to really understand the fundamental principles behind what you're doing. Sometimes you can get away with wrote memorization. e.g. You can come up with equations for a lot of things yourself if you understand Gaussian distributions but, if you're being prepped for an exam by teachers who know roughly what's on it, they might just give you equations to memorize for the things that are likely to be asked. You may perform nearly as well as someone with deep understanding of the material, but you are unlikely to remember those equations long after you've taken the test!
It is quite likely that the person who took and failed this test was the sort of math student who was able to get by memorizing what he was told to without really understanding things. If he had written the same test in high-school he likely would have done much better because he would have been prepared for it with memorized methods and equations that he never understood and has long since forgotten.
On teaching methods:
When teachers teach students to pass tests, short-cuts like wrote memorization tend to happen. The useful knowledge learned from this kind of teaching is minimal. Unfortunately, many teachers are unable to teach the deep meaning behind mathematics because they were taught by wrote memorization themselves. When they were assigned to teach math class they probably had to look everything up themselves since, like our test-taker, they never understood the basis behind it and have forgotten most of what they memorized.
It seems that we must overcome the problem of educating teachers before they can overcome the problem of educating students.