This question is really difficult to answer, I have not encountered such an interview problem before.
The individual thinks the programmer is focused on implementation, and the product manager focuses on the product design. The Division of labour and the nature of the two are not the same as the depth of view of the problem.
I, as a programmer, certainly want to speak for programmers. Product Manager Design product is an idea, can realize they may not fully know. So the product manager in the control of the product direction, a lot of details to listen to programmers. Of course, programmers have to say that a large and empty product is illusory, no programmer there is no blood and meat. There are few thoughtful and practical product managers, who often like to copy other people's designs and move others ' successful cases to their designs. For example, I was working on a social networking site in a company that was completely copy Facebook.
To think that Facebook can succeed in the United States in China. including what technology, how the page design, which features a complete copy, a little unreliable, the number of people from several decades, a few months to find more than 500 people, lasted 1 years before the fall.