I guess I'd reply after some consideration that what I think is unreasonable about this question is just that I as a physicist know exactly how to answer it because I have received years of training in reasoning about things that I don't know and years of understanding error bars and orders of magnitude, so that I can say "well within a half-order it's this."
But I came to know a lot of professional mathematicians in that time, and they are people with very big minds, extraordinarily creative -- but several of them would potentially struggle on these sorts of questions (indeed some of them would struggle with arithmetic, having long since just unloaded that burden onto calculators and computers to free their brain for more interesting thoughts) simply because they're not used to reasoning about uncertainty. They are likely to simultaneously be very good hires, and to only give you the barest of lower bounds. "I mean, it's at least 30 because I can fit 30 in a carry-on. Oh, but there could be a hundred seats and a hundred carry-ons, so I guess it's at least 3000." "It's, uh, it's way more than that." "Right, I said 'at least'. I mean we could probably stuff at least two carry-ons in each seat, so that gets us towards a better lower bound of 9000 or 10,000?" "Yeah, uh, still much much more."
I know other folks who would make great junior or mid-level developers who never had any formal education and wouldn't be comfortable approaching this either from the "let me look up or estimate volumes and recall packing densities" or the "I can give you lower bounds based on the things I am absolutely sure about" approaches. They wouldn't necessarily know, for example, that one might just say "okay let me look up the size of a 747" in an interview, that such a thing is probably "within the rules" of what the question expects -- unless prompted, and even then.
Let me put this a different way, do you think that responses to that question could be improved if before the interview you walked a candidate through a similar problem for ten minutes? Because I would imagine it could be, but maybe you ask it in a way that already provides for that. The problem is that if people can do substantially better with a ten-minute nudge then you are actually just testing for who has already had the sort of life experience to give them that ten-minute nudge, and that doesn't seem like an "excellent question" to me.
But I came to know a lot of professional mathematicians in that time, and they are people with very big minds, extraordinarily creative -- but several of them would potentially struggle on these sorts of questions (indeed some of them would struggle with arithmetic, having long since just unloaded that burden onto calculators and computers to free their brain for more interesting thoughts) simply because they're not used to reasoning about uncertainty. They are likely to simultaneously be very good hires, and to only give you the barest of lower bounds. "I mean, it's at least 30 because I can fit 30 in a carry-on. Oh, but there could be a hundred seats and a hundred carry-ons, so I guess it's at least 3000." "It's, uh, it's way more than that." "Right, I said 'at least'. I mean we could probably stuff at least two carry-ons in each seat, so that gets us towards a better lower bound of 9000 or 10,000?" "Yeah, uh, still much much more."
I know other folks who would make great junior or mid-level developers who never had any formal education and wouldn't be comfortable approaching this either from the "let me look up or estimate volumes and recall packing densities" or the "I can give you lower bounds based on the things I am absolutely sure about" approaches. They wouldn't necessarily know, for example, that one might just say "okay let me look up the size of a 747" in an interview, that such a thing is probably "within the rules" of what the question expects -- unless prompted, and even then.
Let me put this a different way, do you think that responses to that question could be improved if before the interview you walked a candidate through a similar problem for ten minutes? Because I would imagine it could be, but maybe you ask it in a way that already provides for that. The problem is that if people can do substantially better with a ten-minute nudge then you are actually just testing for who has already had the sort of life experience to give them that ten-minute nudge, and that doesn't seem like an "excellent question" to me.