I don't think there are any very difficult questions. You should always ask clarifying questions if something is not clear. I had to ask many clarifying questions.
Manager Project Interview Questions
118,016 manager project interview questions shared by candidates
Where do you see yourself in 5 years
What is your favourite Google Product, and how would you improve it?
Suppose you are working on a project with an original scope of a few months and you are told that you instead now have a few days -- how would you handle it?
The most unexpected question was "What book are you reading right now?" Since I like to read I could answer it easily but if you didn't read much it would throw you for a loop.
If you had a scale and 12 balls and one was weighted, under 3 try's can you find the weighted ball?
If you have a vacant field and add one flower and the number of flowers doubles everyday and at the end of 45 days, the field is full, on what day is the field half full?
Imagine that you are a PM at [big software company], and you are assigned to build [business process] software for [small business vertical]. How would you measure success?
which is more important - team or clients
How and where would I fit in.
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