Estimation questions appear in almost every trading interview, usually as the setup for a make-a-market exercise.
Why they are asked
Not to test general knowledge. They test whether you can decompose an unfamiliar problem, reason quantitatively under uncertainty, and be explicit about assumptions - which is the job.
The method
Decompose into factors you can each estimate to within a factor of two. Estimate each. Multiply. Sanity-check.
The reason this works: independent errors partially cancel. If you overestimate one factor and underestimate another, the product is closer than either. A four-factor estimate is typically accurate to within an order of magnitude even when each factor is shaky.
Worked example
How many petrol stations are there in the UK?
- Population: about 67 million.
- Cars: roughly 0.5 per person, so about 33 million.
- Each car fills up perhaps once a fortnight: about 26 fills per year, so 860 million fills annually.
- A station serves maybe 500 cars a day: about 180,000 a year.
- So 860 million / 180,000 ≈ 4,800 stations.
The true figure is around 8,000. Within a factor of two from first principles, which is a good outcome.
Anchors worth knowing
Having a few real numbers makes everything faster:
- World population ~8 billion, US ~340 million, UK ~67 million.
- Seconds in a year ≈ 31.5 million (pi times 10^7 is a useful mnemonic).
- A typical person lives ~80 years, works ~40.
- Minutes in a day: 1,440.
Sanity checks
Always finish by testing the answer against something you know. If your estimate implies more petrol stations than supermarkets, revisit.
In the interview
Say every assumption out loud. "I'll assume roughly half a car per person - that feels right for the UK." The interviewer may correct you, which is free information, and the assumptions are what is actually being marked.
A wrong answer with clean reasoning scores well. A right answer with no visible reasoning does not.
Practise with the estimation drill.