So, I previously posted a question for you all about piano tuners in Paris, specifically how many are there. It isn't about googling or looking in a phonebook because this was an example of the type of case interview question you might actually get. I promised I'd give you some time to solve it and then share how to handle it. If you haven't seen the original post yet, you can check it out here first. But spoiler alert, I'm telling you how to solve it after the jump (hit read more).
So, if you're at an interview and get asked something like how many piano tuners exist in some random city, how many ping pong balls fit into a school bus, or any number of other seemingly strange and unrelated question, don't panic. The question is not about seeing how great you are at math, testing your psychic abilities, or even requiring you to do a Devil Wears Prada-esque search for the true answer (well, unless you're interviewing with Miranda Priestly). These questions are about problem solving, critically thinking, using logic, and demonstrating an ability to think on your feet.
These questions can generally be worked through using a series of assumptions and estimates. So, to begin with here you would need to assume that there are just as many tuners as the market demands. So, to figure out how many that is you need to make an estimate of the number of people in Paris. Try to keep it reasonable, but you also want to use a number you can easily work with to do math. Let's say 2 million. Then, you need to decide about how many households that means. You would want to try to take into account things like the number that live alone versus the number of families. For our purposes, we're going to pick something simple and say that there are half as many households. Next you need to make an estimate of how many people own a piano. Again, try ot be reasonable but keep your math easy. We'll say 10%. The next step is to decide how often pianos are tuned. Let's say once per year. Then, how many pianos can be tuned in that time span? We can say it takes about 2 hours to tune a piano, tuners have a 40 hour work week, and work about 50 weeks per year. So 20 tunings per week x 50 weeks= 1,000 tunings per tuner a year. Now we know that there 100,000 tunings per years and 1,000 tunings done by each individual tuner in one year. So we can simply divide and get 100 tuners.
I know that can be hard to follow in paragraph form so the steps are outlined a little better below. I admit math has never been a particular strength of mine so feel free to double check it and challenge it. But, it's most important that you understand the concept and can recreate and apply it yourself. If you need more help or examples just ask, I'm glad to go over it again and again. And in the mean time, if you need some more practice, try going through these questions from Google
1) There will be as many tuners as the market demands
2) Assume 2 million people live in Paris
3) Say there are roughly half as many households- 1 million
4) Say 10% own a piano. 10% x 1,000,000= 100,000 pianos
5) 1 tuning per year= 100,000 piano tunings per year
4) 2 hours to tune 1 piano
40 hour work weeks= 40 hours a week/ 2 tunings per hour= 20 tunings a week
20 tunings per week x 50 work weeks a year= 1,000 tunings per year
6) 100,000 tunings per year/ 1,000 tunings per year per tuner= 100
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