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This question was asked at an interview for an FX-options trader position at a Big Four Australian bank.
The question in full
We want you to tell us how many professional piano tuners there are in Melbourne, and walk us through your logic for coming to your final answer.
The candidate’s response
· 4m people in Melbourne
· Average household = approximately three people, therefore 1.3m households
· Households are divided into 1/3 wealthy, 1/3 middle, 1/3 lower-income brackets
· Wealthy more likely to afford a piano. Estimate 45% of wealthy households have a piano, middle 30%, lower 15%: provides average 30% of households have a piano = roughly 400,000 pianos in Melbourne
· Piano needs to be tuned every three years, therefore 130,000 pianos need tuning each year in Melbourne
· Tuning takes 1.5 hours, therefore 200,000 hours of Piano tuning work in Melbourne
· Full-time piano tuner works 40 hours a week, therefore 40 x 52 = 2000 hours worked per year after annual leave
· 200,000/2,000 = 100 piano tuners required to service Melbourne area
Then they asked me how I would go about confirming my logic, and my response was “via the Yellow Pages”.
The answer
They then pulled out the Yellow Pages and told me there were actually about 150 piano tuners in Melbourne.
Did the candidate get the job?
I ended up taking a different role which I was applying for simultaneously, so I exited the interview process before an offer/rejection was made.
What would you say in answer to this question? Leave your response in the comments box below.
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Great answer! Although pianos actually have to be tuned earlier than 3 years if say you move or you don’t position it properly and it is affected by the changing seasons.
Forgot to factor in travel time and “full time” piano tuners don’t work 40 hours. But I’m sure all that detail is unnecessary.
Good work nonetheless!
Thanks for sharing. Nice work!
I will probably adjust the percentage of households with piano lower than 27%. There might be electronic pianos(like my place) or keyboards there and they do not need to be tuned. And a grand piano needs probably once a year service? Other than those I think it was a pretty clean answer :)
I agree with the higer level logic. However two points to include:
1. 2000 hrs a year from a productivity point of view is actually very high, I have in the past used 2000 – statutory & discetionary leave – training etc = aprox 1341 hrs (BAH philosophies).
2. I’d make asumptions such as “How many are actually gainfully employed as a piano tuner:? How many sell, teach, restor and deliver as well as tune?
So out of the 150, the agregate is probably more like 4 full time carbon based units.
Pianos need to be tuned at the very least once a year & many are
tuned several times a year if not a month for professional use. You would
find it difficult to have the service of a properly trained tuner,
they would only be a few dozen who would qualify I’m greater Melbourne
I think the assumption about the wealthy owning more pianos is flawed. I would have assumed that the upper and lower middle classes own at least the same proportion as the wealthy. That assumption would have resulted in pretty much the correct answer.