Prior to the ruling in NYSRPA v. Bruen putting a stop to the practice the LTC application processes in the less permissive towns in Massachusetts were well known to have forms of this sort in addition to the basic state form as well as undocumented "soft requirements" and "nice to haves". In Boston proper you basically had to write an essay, or maybe that was Cambridge, I forget.
This test is a caricature of the type of test mentioned in the post above yours, but yes, on many federal tests I have taken, there are a lot of questions that are intentionally tricky or have no correct answers, only less wrong ones.
Most notably, pilot examinations for aviation and maritime certifications.
I think they use these types of questions to exclude rule memorisation and test the ability to reason about the intention or relevant effects of rules and principles of the art involved.
It seems like the intention is also to penalise the inability to reason about ambiguous situations, ensure that the subject can effectively divide attention (if you spend too much time focusing on these ambiguous situations trying to find a nonexistent perfect answer you will fail the test), and to filter out low cognitive ability in general.
