"Make me a market on the number of petrol stations in Germany" is the defining trading-interview question. It is not a trivia test.
What you are being asked
Give a bid (the price you will buy at) and an ask (the price you will sell at). The interviewer may then trade against you on either side, repeatedly, and may tell you things as they go.
You are being scored on four things: whether your midpoint is sensible, whether your width reflects your uncertainty, whether you manage your position afterwards, and whether you update rationally on new information.
Step 1: estimate the mid
Do a quick Fermi estimate out loud. Germany has about 84 million people; perhaps one station per 3,000 people; that suggests roughly 25,000-30,000.
Say the reasoning. A wrong midpoint with visible logic scores far better than a right one pulled from nowhere.
Step 2: choose a width
Your spread should be wide enough that you are comfortable being hit on either side, and no wider.
For an estimate you are confident in, quote maybe 10% either side. For one you are genuinely unsure about, quote much wider - 14,000 / 40,000 is a perfectly respectable market on a number you barely know.
The two errors:
- Too tight: the interviewer trades against you and you have no margin. This is the more common one, driven by wanting to look confident.
- Absurdly wide: quoting 1 / 1,000,000 avoids risk but shows nothing and interviewers will call it out.
Step 3: honour it
If they say "I buy 100 at your offer", you are now short 100. Say so out loud. Then re-quote - and your new quote should shift, because you have inventory you would like to reduce. See inventory risk.
Step 4: update on information
If they say "the actual number is above 20,000", move your market. Failing to update is worse than a bad initial quote. So is moving in the wrong direction.
The most common failure
Not the pricing - the bookkeeping. After six trades, candidates routinely cannot say whether they are long or short. Track it explicitly and out loud: "I'm short 300 at an average of 27,000."
Practise with the market-making game.