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I have a favourite PM case study question that I'm retiring today. I'll write up the question and the best answers I've heard in this thread.

This case study has been the highest signal, under 20 minute question I can ask potential PMs.
Question: Find a water bottle. You have one? Great. Tell me how you would improve it.

I always ask that question in that exact same way. “Tell me how you would improve it.”
The PMs that pass this test all start by recognizing that they need to first ask “improve for whom?” If you jump right into saying “I like this”, you have failed miserably.
The best candidates say there are 5 potential users: 1) users drinking water from the bottle, 2) buyers of the bottle, 3) those who manage logistics of moving/storing bottle, 4) people who sell the water bottle and 5) manufacturer. If you get 3 sets of users, you’ve done well.
Some good, but not great, candidates immediately jump into describing three or four types of end users (athletes, office workers, etc.) That’s okay. But not great.
Having described the set of users, the best candidates then go through a “jobs for people” process and describe what these users are looking for in a water bottle.

The candidates I fall in love with immediately narrow down to two sets of users and go through trade offs.
They pick one and describe the downsides of picking that user.

They then say “this is how I can most quickly test if I’ve picked the right user.” And describe how they would measure the answer to that question and set out the next two or three steps they would take.
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