For harder tests, the benefit is in not ignoring low-hanging fruit, and training to look for any opportunity to get better reliability, performing cheap checks and selecting more reliable of any alternative sub-steps. On the other hand, ordinary exams are often such that a well-prepared applicant can solve all problems in half the time or less, and then the failure would be not taking advantage of the remaining time to turn "probably about 90% of solutions are correct" into "95% chance the score is perfect".
Gotcha. That's much more clear to me - thanks.
Lately I've resolved to try harder at teaching myself math so I have a better shot at the international olympiad (IMO). These basically involve getting, say, three really hard math problems and trying your best to solve them within 5 hours.
My current state:
What does the intrumental-rationality skill of LWers have to say about this? What recommendations do you guys have for improving problem-solving ability, in general and specifically for olympiad-type environments? Specifically,