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Quant interviews test a small set of skills again and again: probability, expected value, quick arithmetic, clear reasoning out loud, and, for some roles, statistics, code or derivatives. This page sorts those skills into seven question sets, each with a worked example, problems to try and where Thuztra Learn teaches it. Then it gives a six-week plan.
Practise now, free: the market making game. Ten timed rounds on dice, coins and cards, with the exact fair value and the reason after each quote. No account.
The same question types turn up in the US, the UK, continental Europe and India. The mix depends on the role more than on the country. Formats differ from firm to firm, so read the table as a rough guide, not a rule.
| Role | Where | What the rounds lean on |
|---|---|---|
| Trader at a market maker or prop trading firm | Trading firms and proprietary desks | Mental maths, probability, market making games and betting |
| Quant researcher | Hedge funds and systematic asset managers | Probability, statistics, research discussion, often coding |
| Quant developer | Trading firms, funds and banks | Coding and system design, numerics, some probability |
| Desk quant or strat | Banks and pricing teams | Derivatives, stochastic calculus, numerical methods |
In India, many quant roles are filled through campus hiring, which often opens with an online test of maths, probability and coding before any interview. Elsewhere, an online test or a phone screen is also a common first round. Either way, the sets below are what those first rounds draw on.
The core of almost every quant interview. Counting, conditional probability, Bayes' rule and expected value, asked as dice, cards and coin problems you solve in a few minutes without a calculator.
Question. You draw two cards from a shuffled 52-card deck. What is the chance both are aces?
Answer. The first card is an ace with chance 4/52. Given that, the second is an ace with chance 3/51. Multiply: 4/52 × 3/51 = 12/2652 = 1/221, about 0.45%. Check it another way: there are C(4,2) = 6 pairs of aces out of C(52,2) = 1326 pairs, and 6/1326 = 1/221.
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Where Thuztra Learn teaches it: Probability from zero · Level 1: First instincts · Level 1: The expectation toolkit · Probability from the ground up.
Puzzles with no formula to look up: weighings, switches, fuses, crossings. The interviewer watches how you search. Do you try a small case, find what stays the same, and say when a path is a dead end?
Question. You have a 3-minute sand timer and a 5-minute sand timer. Measure exactly 7 minutes.
Answer. Start both at minute 0. At minute 3 the small one runs out: turn it over. At minute 5 the large one runs out. The small one has now run 2 minutes of its second turn, so 2 minutes of sand sit in its bottom half. Turn it over: those 2 minutes run back through, and it empties at minute 7.
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Where Thuztra Learn teaches it: Level 1: First instincts · Level 1: Stopping, games and edge.
Common at trading firms. You quote a bid and an ask on something uncertain, the interviewer trades with you, and you move your quotes. Betting games ask how much to stake when you have an edge, and when to stop.
Question. Make a market on the sum of two fair dice.
Answer. The fair value is 7, since each die averages 3.5. The standard deviation is √(2 × 35/12) ≈ 2.42. A market of 6 to 8 holds the fair value and is under one standard deviation each side. If the interviewer buys at 8 again and again, ask why: they may know something, such as a die that is not fair. Move both quotes up, and say why out loud.
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Where Thuztra Learn teaches it: How prices actually form · Market making and inventory · Position sizing and risk taking · Level 1: Stopping, games and edge.
Some trading firms open with a timed arithmetic test, and every interview rewards fast, safe estimates. The skill is less raw speed than knowing a few shortcuts and checking the size of the answer.
Question. 17 × 23, in your head.
Answer. Both are 3 away from 20, so this is (20 − 3)(20 + 3) = 400 − 9 = 391. Another one: 7% of 340 is 7 × 3.4 = 23.8. And money doubles at 5% a year in about 72 ÷ 5 ≈ 14 years (the exact answer is ln 2 ÷ ln 1.05 ≈ 14.2).
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Where Thuztra Learn teaches it: The school maths, rebuilt · Money maths from zero · Level 1: First instincts.
Most important for research roles. Estimators and their bias, regression, testing many ideas at once, and whether a backtest result is real or luck.
Question. A strategy's daily returns have a standard deviation of 1%. Roughly what is the yearly standard deviation?
Answer. If days are independent, variances add, so the yearly SD is 1% × √252 ≈ 15.9%. Traders round √252 to 16. The answer leans on independence: if returns trend from day to day, the true number is larger.
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Where Thuztra Learn teaches it: Data from zero · Level 1: Estimates, tails and desk numbers · Estimation theory · Statistical inference for research.
Central for developer roles, and present in most others. Clean code under time pressure, plus numerical sense: why a formula that is right on paper goes wrong on a computer, and where the time goes.
Question. A service computes variance as mean(x²) − mean(x)², and sometimes reports a negative number. Why?
Answer. Take values near 1,000,000,000 that differ by about 1. Their squares are near 10¹⁸, and the two terms agree in about their first 18 digits. A double holds about 16 significant digits, so the difference is rounding noise and can come out negative. Subtract the mean first (a two-pass method), or update the mean and variance one value at a time (Welford's method).
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Where Thuztra Learn teaches it: Python and vectorisation · C++ where it earns its place · SQL for time series · Performance and profiling · Monte Carlo and variance reduction.
Asked most in desk quant and pricing roles. No-arbitrage arguments, put-call parity, Ito's lemma and the Greeks: can you derive the result, not only recite it?
Question. A stock trades at 100, pays no dividend, and the one-year rate is 5% with continuous compounding. What is the one-year forward price?
Answer. Borrow 100, buy the stock, and hold it for a year. You owe 100 × e^0.05 ≈ 105.13. Any other forward price lets someone lock in a riskless profit, so the forward is about 105.13.
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Where Thuztra Learn teaches it: Level 2: Model making · Brownian motion and Ito calculus · No-arbitrage and risk-neutral valuation · Options and volatility trading · Greeks and implementation.
About 8 hours a week (our estimate). Shift the weeks toward your role, and start earlier if probability is new to you: why probability comes first, with a free course for it.
Thuztra Learn teaches the maths of quant finance from zero, in short lessons, for readers who are unsure of it. Three questions in the app build your quant roadmap, free. Membership is a paid subscription. See what Thuztra Learn is and what it costs, or see the whole Core quant curriculum.
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