At what point is it appropriate to just ask for figures in a market sizing question?

You are not supposed to ask for any figures in market sizing questions.

You could say based on xyz, I'll assume that the area is this big. If you are way off, the interviewer may correct you. That's why the interviewer doesn't care about you being factually correct, he only cares about your logic. Use references, e.g., you know how tall the Rockfeller center is, and you know it's considered rather tall, hence you assume that Eiffel would be maybe 50% of that height. You can't just say I don't know, tell me. You must have seen the Eiffel tower hundresds of times on pictures.

To give you an example, you can calculate the area of USA by using the following assumption:

• The airplane flight time from NYC to SF is about 5 hours
• The plane speed is 600 miles/hour
• USA is like a rectangular in the area. Vertically USA is about half of USA horizontally. The size of the rectangular is a*b, where b=a/2.
• Calculation: USA area = a*a/2 = (5 hours * 600 miles/hour) * (5 hours * 600 miles/hour) / 2 = 3,000 * 3,000 / 2 = 4.5 million sq miles. The actual area is 3.8M. You are off by 18% here, that's totally reasonable.