Problem-solving/product question is something that you'll come across in every PM interview. Here's a way on how shall one approach it. (Not my technique, an amalgamation of the best possible ways)
Read the summary again- As I mentioned, the idea is to help on “how shall one approach the question”. We need to understand that every time the interviewers are not looking just at the solution. It’s how does one reach those solutions also matter. Having said that, I am not trying to undercut the importance of a good solution that moves the needle for the product in a significant manner. (We will come to this)
Question Type: There are different versions of this but broadly these question looks like the one mentioned below:
Skills being looked for: how do you think, strategize, prioritize and design the features
Don’ts: Again, before we jump into what to do, most important is what not to do
  1. Please do not directly jump into solutioning and start throwing solutions features.
  2. The features/solutions suggested should not on the lines of visual element changes or an incremental feature. The solution should fundamentally impact the product and its users. Additionally, the feature should have a significant desired impact. (moving the needle)
Solving framework:
First, I’ll discuss the problem in depth to make sure I understand it correctly. Then we can discuss the business situation and our objective in details. Subsequently, I will focus on defining the target user and brainstorming what problems we could solve for them. And lastly, I will try to generate solutions for these problems, prioritize them, and make a recommendation .
Side Note