I got as far as the second question and then decided I was smarter than the test's author. "How many months have 28 days?"
Obviously we all read that and know it is supposed to be a clever trick - "OMG! 'Cause like months that have 31 days totally also 28 days". But seriously? Every native English speaker naturally interprets that question to mean "how many months have exactly 28 days" and the question author fucking well knows that they're phrasing the question badly. They even set it up that way in their own phrasing with "some months have 30 days, some months have 31 days" implying that the latter case is distinct from the former case when in fact the correct wording EVEN IF YOU WERE USING THE QUESTIONER'S INTERPRETATION would be "some months have 30 days, some months also have 31 days". It's badly phrased twice over even within itself. I loathe questions that rely on their own ineptness with phrasing. If you want to test my actual ability with something, test it. Stupid little gotchas like that are obvious and for petty people.
The one about "how many nines between 1 and a 100" is also another stupid question. There is one. Obviously they mean how many times does the digit '9' appear in representations of all the numbers between 1 and 100, but to anyone with a programming / mathematical bent (which I will willingly argue is the more accurate way to think), the answer that immediately occurs is that there is 1. 9 is not 19, however you write it down.
The smartest people? Those that realize the test is only testing their willingness to wilfully go against the normal meanings of language. No-one can claim the test author isn't knowingly phrasing things in a way that isn't natural to the English language.