Does that problem not require separate thought processes though?
In terms of a max/min/mean/median style problem, the candidate needs to come up with an algorithmic solution to find those values. In the later case of finding duplicates, there is minimal (depending on problem complexity, I suppose) amount of algorithmic complexity and the focus is more on data structures; for instance, does the candidate know they could use a data structure like a hashmap or variant to find unique items with the drawback being an additional storage unit.
So, I guess what I'm trying to trace back to is how you say if they can't answer one then surely they can't solve the other, but (while relatively 'simple' problems) I'd argue they take different mindsets to solve. Obviously in the grand scheme of things one mindset works for both, but in this it can vary a bit.
Anyway, late-night thoughts so hopefully that's not a jumbled-up response.