In Hungarian, the third person pronoun "Ö" does not designate gender. Because it is gender-neutral, I answered, "He/she is a musician, not a waiter." My answer was marked as incorrect because I used an incorrect word (she). We do not know if the musician is a male or a female. It is, therefore, incorrect to translate "ö" only as "he".
(In some places, it is slowly becoming accepted to use "they" as a gender-neutral option in English for "he" or "she", even though it is plural.)
The problem here in Hungarian there is less information in that sentence than in English, so it's makes harder to translate.
1) Ő (egy) zenész nem (egy) pincér. -> Neither of the words contain anything to refer any gender.
((As far as I know in the old times it was obvious who is who, but later we did not develop words to differ, or we did not keep that habit))
2) (In this situation!) Depending on giving "a/an" it could have a slightly different meaning, but we do not really care when we talk... so don't bother much, as far as you get "the"(a/az) and "a/an"(egy) right.
-a curious Hungarian who checked on this ;)