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I have no idea what it is like now but a significant part of the testing environment at Georgia Tech in the early '80s in the highly competitive engineering fields was "impossible" exams. These involved a timed in-class exam of an hour (sometimes two) where it was not possible to solve the major points problems analytically within the time limit, but a variety of approximation techniques were available. The highest scores came from understanding how to deploy the fastest approximation techniques.

Unlike many of my classmates I was really good at the mathematical part of the exam questions and could straightforwardly solve them analytically. However, this took too much time! I bombed several important exams learning that "good enough" is an important attitude to have when solving engineering problems. I hated this intensely at the time. (Never give that Stalinist institution a dime till I die.) BUT. There's a reason I went into numerical analysis in graduate school. Which I loved then, turned into a transient career that I enjoyed immensely, and remember fondly.

I doubt this approach is feasible for non-engineering disciplines.

[edit: redundancy removal]