While the point behind posting these entrance exams is often to make a commentary on a decline in education standards, I'd suggest that it really shows nothing of the sort. The exam is, in fact, rather easy and simplistic, and only seems difficult because of different priorities.
The grasp of Latin and Greek required for the language portions is minimal. This is particularly the case because, for the translation portions, all vocabulary is provided, including words that should be instinctively known by anyone with any grasp of the languages (esse in the first question!? καἰ?). Any foreign language test today would be significantly more difficult.
The mathematics section looks intimidating only because it involves dealing with difficult numbers by hand. There are specific techniques that would have been taught to work through such problems efficiently, but teaching them now isn't particularly useful. Conversely, the more conceptual and abstract questions are very simple: asking what a prime number is? Asking why exponents are added under multiplication?
The history and geography section, meanwhile, is mainly concerned with regurgitation of facts covering very narrow sections of the subject. Perhaps the question asking for the difference between Athens and Sparta could allow some deeper discussion, but most do not.
Overall, the test is focused on questions about specific topics requiring memorization rather than questions testing deeper insight and understanding. It's not something that should be looked back on as some product of a better age.