Product design questions test the applicant's ability to think on their feet and create a full product or feature. New product design questions can be very high level ("design a lamp"). Start with identifying the goal of the product-if the interviewer won't tell you, state your assumptions so that you have something to build on. Decide which metric or business driver you will impact most. From there, identify the possible users for the new product or feature. Select the one that seems most relevant.

You won't have time to cover everything in the answer. Once the user is selected, move on to use cases, goals, and scenarios for that user. The use cases should naturally result in a set of features for your new product. Prioritize these and close by linking back to the goal of the product, the business strategy, and the user needs you are meeting. Show you aren't afraid to color outside the box by including a range of features in the product or tackle a novel problem. Present a range of ideas ranging from mundane to outlandish and demonstrate that you can generate a broad range of ideas and decide among them quickly.