Why I wrote 554 practice questions and gave them away

A student asked me last year to explain conditional expectation. I said the thing I always say, the thing about the tower property, and watched it not land. So I wrote out a problem. Then another, because the first one let him get the right answer for the wrong reason. By the fourth he said "oh" in the way people do when something has actually moved, and I realised I had spent forty minutes writing questions to replace two minutes of explanation.

That kept happening. The explanation was never the bottleneck. The bottleneck was that he had seen four examples and needed thirty.

Why there are so many

Most free question sets are small, and the ones that are small are small for a reason: they exist to demonstrate that a paid product is good. Twenty questions is enough to prove competence and not nearly enough to build any. You work through them, feel briefly encouraged, and hit the paywall at exactly the point the material was starting to bite.

The number that actually helps is uncomfortable. To be at ease with conditioning you need to have been caught out by it a dozen times in a dozen different costumes — the boy-girl problem, the medical test, the two envelopes, the one where the weekday looks irrelevant and moves the answer. Each one fails differently. You cannot get that from five.

So the probability bank has 88 questions rather than 20, and the brainteaser bank 69, and the whole thing 554. Not because more is better as a principle. Because the number where it starts working is higher than anyone wants it to be.

Where the questions came from

Every one is written from scratch. That is not a legal disclaimer, though it is also that — question banks are copyrighted and lifting them is both wrong and obvious. It is that writing a question forces a decision you can otherwise avoid: what, precisely, is this testing?

A question copied from somewhere is a question whose purpose you have not examined. You reproduce the surface and lose the reason. When you write it yourself you have to pick the numbers so that the tempting wrong answer is genuinely tempting, and that is most of the work. The Monty Hall problem is not hard because the arithmetic is hard. It is hard because the wrong answer feels obviously right, and a version with the numbers changed carelessly loses exactly that.

The models were the books that do this well — Mosteller for probability, Kordemsky for the puzzles. Not their questions. Their register: a short statement, a surprising answer, and a solution that turns on one idea rather than three pages of algebra.

The solutions are the actual product

A question with the answer at the bottom is worth very little. You either got it or you did not, and if you did not, "the answer is 13/27" tells you nothing about where you went wrong.

So the solutions say what the decisive move is, and then why it works, and then — where there is one — the thing that generalises. The 100-prisoners problem is not really about prisoners; it is about correlating your failures instead of reducing them, and once that has been said out loud you start seeing it elsewhere. That last sentence is the part worth keeping, and it is the part a bare answer key cannot give you.

A few solutions are longer than the question by a factor of five. That is the right ratio.

What it costs me, and why I do it anyway

Nothing about this is charity. I make my living preparing people for quant interviews, MBA admissions and Oxbridge entry, and those engagements are expensive. The bank is the most honest advertisement I can run: you can work through several hundred of my questions, read several hundred of my solutions, and form a view on whether I am any good before we ever speak.

That filter runs in both directions, which is the part I actually value. People who arrive having done forty of the probability questions already know what they are weak at. The first call is twenty useful minutes rather than twenty diagnostic ones. And people for whom I am the wrong choice work that out for free, on their own time, without a sales conversation.

Compare that with the alternative, which is a landing page asserting that I am rigorous. Anyone can write that sentence. Very few people will write 554 questions to back it up, and that asymmetry is the whole point.

The mistakes, since they are instructive

I have pulled questions after publishing them. One tiling problem had a proof that was really a confident assertion in the shape of a proof — the colouring argument did not close, and I had not noticed because the answer was right. Another contradicted itself between the working and the stated answer. A third turned out to be a third question testing the same Fibonacci recursion.

All three are gone. I mention it because "554 questions" invites the assumption that they were generated, and the reason they were not is precisely that generated questions fail in this way and nobody checks. There is now a script that scans the whole bank for near-duplicates before anything ships, which exists because I shipped duplicates.

What is actually there

Six quant banks — probability, brainteasers, stochastic calculus, statistics and machine learning, market making, mental arithmetic. GMAT Focus Quant and Data Insights, and GRE Quant and data interpretation, each question carrying the percentile it sits at. Oxford MAT, TMUA and STEP at real admissions-test level. And a coding course with problems solved in six languages, every solution compiled and run before publication.

Each bank has a timed mode that reproduces the real exam's pacing, because knowing how to do a question and being able to do it in ninety seconds are different skills, and only one of them is tested.

No account. No email form. Start anywhere:

All 809 questions The coding course

One caveat

Questions are not preparation. They are the part of preparation you can do alone, which is most of it but not the hard part. The hard part is being asked something you have not seen, out loud, by someone who interrupts, while you think in front of them. Nothing on this page simulates that, and anyone telling you otherwise is selling something.

Do the bank. It will make you better. Then find someone to sit across from — me, a friend who has done the job, anyone who will push back — because that is the bit that decides the outcome.