Estimation round, common for trading roles.
Estimate the piano tuners
The question
How many piano tuners work in New York City?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
A defensible estimate in the low hundreds, with your assumptions stated.
Decompose: population about 8 million, roughly 2.5 people per household, so about 3 million households.
Say 1 in 50 owns a piano, giving 60,000 pianos, tuned on average once a year.
A tuner handles perhaps 4 a day, 250 days a year, so 1,000 tunings each. That implies about 60 tuners, and adding institutional pianos in schools, churches and venues pushes it toward a hundred or two.
No interviewer is checking the answer. They are checking whether your decomposition is clean, your assumptions are stated rather than smuggled, and whether you sanity-check the result at the end.
What it is testing
Structured estimation under uncertainty, and comfort saying a number out loud.
Try these next
Two ropes, forty five minutes
Warm-upTwo ropes each burn for exactly one hour but not at a uniform rate. Using only these, measure forty five minutes.
One hundred prisoners and one hundred boxes
HardOne hundred prisoners must each find their own number among one hundred boxes, opening at most fifty each, with no communication. All must succeed. What strategy beats 2^-100?
One thousand bottles, one poisoned
StandardOne of one thousand bottles is poisoned, and the poison acts in exactly one day. How many testers do you need to identify the bottle in a single day?
The blue-eyed islanders
HardOn an island everyone sees others' eye colour but not their own, and anyone who deduces theirs is blue must leave that night. A visitor says aloud 'at least one of you has blue eyes'. With one hundred blue-eyed islanders, what happens?
Preparing properly
Live opportunities
Interviewing soon? See who is hiring
Open vacancies we track at quant firms, grouped by role and city. Adverts are anonymised.
Hiring for these roles? Brief the desk on a hire or check your fit for a role.
Research desk
Speak to a quant market specialist
Ask what a firm really pays, how a desk hires, or where your profile sits. One reply from the research desk, in confidence, no obligation.