Here’s another recent example of a PM take-home assignment.
This assignment evaluates a PM’s UX skills. It’s very challenging; UX design is not trivial even for UX experts.
And while the assignment doesn’t say it explicitly, showing alternate designs, with a wireframing tool, is what the interviewer expects. And a lot of PM candidates don’t feel comfortable using wireframing tools.
PS I’ve got more tips about take home assignments in my book, Secrets of the Product Manager Interview.