This whole quiz doesn't make any sense. There's 2 things wrong with it:
1. Why will gon, leorio and kurapika all get disqualified if only 1 one of them answers incorrect? Everyone should be questioned individually. And also why didn't the answer of the random guy affect gon, leorio and kurapika? Makes no sense at all.
2. The quiz in itself is logically not possible to answer. She says there are only 2 options to answer, but actually there is a third, silence.
Well, then she should have said there are 3 options: 1-" son", 2-"daughter", 3-"nothing/silence/no answer".
But no, she said there are only 2 options, so of course one would decide to pick one of them, better than nothing.
The whole hunter exam is really flawed, many of the stages have such stupid vague challenges. It all depends on the individual. Just because one does not get that "tricky" question doesn't make him a bad hunter. Leorio is the best example, because he basically got the hunter license out of pure luck. He isn't really qualified to have it.