A quant interview study plan: eight weeks to the final round

Most people prepare for quant interviews by reading solutions. It feels like progress and it mostly is not. Recognising a solution and producing one in front of an interviewer, out loud, in four minutes, are different skills, and only the second is tested.

This is the plan I would follow, as someone who works as a high-frequency trading quant and has been through these interviews as a candidate. It is built around doing, with a measurable bar at the end of each week, and it uses the free practice on this site where that helps.

What you are preparing for

The shape is similar across trading firms, even if the weighting differs. First an online assessment: usually timed arithmetic, sometimes a numerical reasoning test, a game or a coding task. Then one or more phone or video rounds on probability and brainteasers, sometimes with a market-making game. Then a final round of several interviews, often in one day. Trading roles lean on arithmetic and games; research roles lean on statistics, machine learning and code. The firm pages go into detail for Jane Street, Optiver, Citadel, Five Rings and IMC.

The plan at a glance

Two habits that run through all eight weeks

Ten minutes of arithmetic, every day, timed. Speed at mental arithmetic comes from daily volume, not from a weekend of cramming, and the arithmetic screen is where most trading applications end. Use the mental maths tests: the 80-in-8 format candidates describe for Optiver, a 60-in-6, a Zetamac-style sprint and number sequences. Every question is generated fresh, so your score measures skill rather than memory.

An error log. Every question you miss goes into a list with its topic and one line on why: a wrong setup, an arithmetic slip, a missed symmetry, time. Read it on Sunday. After three weeks it will tell you which week of this plan to repeat, which is more than any general advice can.

Weeks 1 and 2: probability, from the ground up

Start lower than you think you need to. Counting (combinations, and the stars-and-bars trick), conditional probability and Bayes' rule, independence. Candidates with strong degrees skip this and then lose points on a conditional probability question they would have got right in their first year, because they rushed the setup.

Week 2 is expectation, the single most examined idea. Two tools do most of the work. Linearity of expectation with indicator variables, which turns "how many fixed points does a random permutation have?" into one line. And first-step analysis: name the states, write one equation per state, solve. The classic is the expected number of rolls until two sixes in a row. The answer is 42, and the worked version shows the setup an interviewer wants to hear.

Practise from the probability bank, easy and medium first. Set a timer for ten minutes before you let yourself look at a solution.

Week 3: brainteasers

Brainteasers test whether you look for structure before you compute: a symmetry, an invariant, a way to make the problem smaller. The brainteaser bank has the classics and some less familiar ones. The skill to practise this week is talking while you think. Say what you are trying, and why, before you try it. An interviewer can help a candidate who is visibly reasoning. They cannot help one who has gone quiet.

Week 4: markets and betting

Expected value of bets, when to take one and how much to stake, and the market-making game: you are asked for a bid and an offer on something uncertain, then traded against, and asked to update. What is being tested is whether your width reflects your uncertainty and whether you learn from being hit. The market-making bank covers the standard forms. Play it with a friend if you can; the updating is the part you cannot rehearse alone.

Week 5: the week that depends on the role

Trading roles: more speed. Move from the 80-in-8 to the 60-in-6 and the number sequences, work through the mental arithmetic bank for the shortcuts behind each type, and play more games.

Research roles: statistics and machine learning. Regression and what its assumptions buy you, overfitting and how you would detect it in a backtest, bias and variance. If the role asks for it, the basics of stochastic calculus: Brownian motion and Itô's lemma. Not before the probability is solid. It is rarely the advanced material that sinks a candidate.

Week 6: code

Research and developer roles almost always have a coding round, and many trading roles do too. The problems are pattern-based: hash maps, two pointers, sliding windows, heaps, dynamic programming. Learn the pattern and its template rather than a hundred individual problems. The coding track teaches it that way, with solutions in six languages, and the timed coding interview gives you a report at the end.

Week 7: timed papers

Now everything goes under a clock. Sit a firm-style paper every other day: Jane Street, Optiver, Citadel, Five Rings and IMC. On the day between, rework every question you missed from a blank page, without the solution beside you. That rework is where the week's learning happens.

Week 8: mock interviews

Out loud, with someone who will interrupt you. If nobody is available, record yourself and watch it back, which is unpleasant and effective. Practise the moment you are stuck. What you do in the ninety seconds after "I don't know" decides more final rounds than any single question; what a quant interview is actually testing is about exactly that.

If you have three weeks, not eight

Compress, but do not cut the end. Week one: probability and expectation. Week two: brainteasers and markets. Week three: timed papers and mocks. Keep the daily arithmetic throughout. Cutting the timed practice to make room for more topics is the most common way to arrive knowing a lot and performing badly.

Three books worth owning

Xinfeng Zhou's A Practical Guide to Quantitative Finance Interviews (the "green book"), Timothy Falcon Crack's Heard on the Street, and Frederick Mosteller's Fifty Challenging Problems in Probability. Candidates and interviewers have both read them, which is exactly why you should: their problems do come up, and an interviewer who spots a memorised answer will move to a harder variant.

Questions people ask

If you have a first round booked and want a plan built around your own error log, that is what the preparation programme does, and a first conversation takes twenty minutes.

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