A couple of comments about the question itself.

It describes the numbers **between **1 and 200 - many would interpret the preposition ‘between’ as a set which is non inclusive of the boundary values, therefore such a question in a competition would be expected to explicitly state whether or not the set of numbers included 1 and 200.

Secondly, stating 200 as the upper boundary of the set is redundant. Most maths questions (as opposed to puzzles) are stated as purely and economically as possible. If the question had been posed as - counting from 1 as the first number, what is the 95th number which is not a multiple of 3 or 5, it would have taken less time to solve (not a big deal in most scenarios but certainly would be significant in selective school tests and the AMC where every second counts as most candidates don’t finish these papers).

IMO, if the question intends to test reading skills and ability to filter the relevant info (ie. inclusion of 200 as the upper limit is a deliberate red herring), then more attention should have been given to grammatical aspects of the question (ie. explicit description of the set), so if it was in an actual scholarship test, it was a poor question. Last year during COVID lockdown, my son had an interesting WFH job, as a quality checker of some Yr 11 & 12 maths practice papers. His employers only asked him to check the answers, but he ended up finding several flaws in the questions in addition to a couple errors in the answers (which the other checkers missed).