Fermi questions are questions designed to test your logic, and you may have encountered them before. So, they usually are formed or phrased in a way where the person asking you this question designs a scenario, asks you about a real world scenario, and asks you to provide an estimate very quickly. Here are few examples. Try to solve these 🙂
http://www.physics.uwo.ca/science_olympics/events/puzzles/fermi_questions.htm
http://mathforum.org/workshops/sum96/interdisc/sheila1.html
http://mathforum.org/workshops/sum96/interdisc/fermicollect.html
http://mathforum.org/workshops/sum96/interdisc/classicfermi.html