I hope these aren't real. I, and most people here, could probably write these codes top to bottom on paper without an eraser or strikethrough parts because we have it fully solved before the interviewer finished the sentence.
Sure, programming is hard if you've never worked with programming language features before... Modulus isn't some obscure esoteric operator, it's literally CS 101
I fell backwards into programming and did it for years before ever needing or encountering a mod operator. It never really came up in statistical programming (SAS) and since I wasn't a CS major I don't think I even learned about it until taking online programming classes for fun. But I know I was a pretty damn good SAS programmer. I never had any issues solving any problems in my field programmatically, but I took a few leet code tests and was completely puzzled before taking said CS classes. The algorithms and common problems just never remotely came up. I never found fizzbuzz particularly relevant in statistics and data CRUD.
Now maybe since SAS is procedural and not OO you'd say it doesn't have typical "programming language features", but I could easily see that experience being common in all kinda of business side programming like R, VBA, maybe JavaScript or Python, etc.
...but anyway obviously I'm not saying its not a good thing for a dev shop to interview on, and if they want someone classically trained then it's probably a perfect question. My quibble is just that you might need to widen your definition of who programs.
Is it? I would expect someone to come up with either toggling a variable back and forth for even/odd, or counting by 2s, heck, treat it as a floating point, divide by two, and search the string representation for a period or something!
Shouldn't people familiar with integer arithmetic should be able to struggle to something like x == 2 * (x/2) to test if it is odd or even? Or just bitwise x & 1?