For example, on (non-cryptographic) hash-functions my answer was to not do them yourself, because they would always be pretty bad, and to instead use the ones by Bob Jenkins, or if things are slow because there is a disk-access in there to use a crypto hash. While that is what you do in reality if you have more than small tables, that was apparently very much not what they wanted to hear. They apparently wanted me to start to mess around with the usual things you find in algorithm books.
No offense, but "I'd rather just use a library" seriously brings into question what you bring to the table and whether you'll just be searching experts-exchange for smart stuff other people have done..Like everybody knows you shouldn't use homegrown cryptographic algorithms, but if a cryptologist can't tell me what an S-box is and points me to using a library instead it doesn't really tell me anything about his skill, except he didn't want to answer the question. In fact, dodging the question like that would be a pretty big red flag.
Don't get me wrong, you can get there. But start off with roughly what you'd do if you had to implement it from scratch, what's difficult to get right, then suggest implementations you know or alternative ways to solve it. Because they're not that stupid that they think this is some novel issue nobody's ever looked at before or found decent answers to. They want to test if you have the intellect, knowledge and creativity to sketch a solution yourself. Once you've done that, then you can tell them why it's probably not a good idea to reinvent the wheel.