Quant interview preparation

Questions

100

Traced to a firm

53

Firms

15

Updated

September 2026

Asked at

All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4DED.E. Shaw3Jane Street3ACAQR Capital Management2DRW2Millennium Management2Schonfeld2SCSquarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1

Topic

All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7

Level

AnyCoreIntermediateHard

Type

AnyBrainteaserTechnicalCaseMarket viewFit

1. 023Monty Hall. Three doors, one car, you pick one, I open a door with a goat, do you switch?ProbabilityCorephone / first roundProp trading firmsQuant trading

   Say this

   Switch. Your original door wins one third of the time, so the other door wins two thirds. The host's choice is not random, and that is where the information comes from.

   Then walk it

   1. Condition on your first pick. One third of the time you picked the car, and switching loses. Two thirds of the time you picked a goat, the host is forced to reveal the only other goat, and switching wins.
   2. So switching wins two thirds. The Bayes calculation agrees: the likelihood of the host opening door 3 is 1/2 if the car is behind your door 1, and 1 if the car is behind door 2, which is what tilts the posterior two to one.
   3. The intuition people find convincing: extend it to a hundred doors. You pick one, the host opens 98 goats, and switching wins 99 times out of 100. The host did all the work of avoiding the car.
   4. The critical assumption, and this is what a quant interview is really checking: the host knows where the car is and always opens a goat. If the host opens a door at random and happens to show a goat, the posterior is fifty-fifty and switching gains nothing.
   5. So the honest answer is: switch, and the reason it works is that the host's constraint leaks information. Change the host's rule and the answer changes.

   Where candidates lose it

   Getting the right answer for the wrong reason, or failing to state the host's rule. Everyone knows the answer is switch, so the only thing being graded is whether you can name the assumption that makes it true. Say explicitly that the host knows and is forced to reveal a goat.

   Expect next

   • What if the host does not know where the car is?
   • What if the host only offers the switch when you picked the car?
   • Do it with a hundred doors.
2. 032How many people do you need in a room for a better than even chance that two share a birthday, and why is the answer so small?ProbabilityCorephone / first roundProp trading firmsQuant trading

   Say this

   Twenty-three. The reason it feels small is that you are counting pairs, not people. Twenty-three people generate 253 pairs, and each pair matches with probability 1/365, so you expect about 0.69 matches.

   Then walk it

   1. Compute the complement: the probability all birthdays differ is 365/365 times 364/365 times down to 343/365. At 23 people that product is about 0.493, so the match probability is about 0.507.
   2. The back-of-envelope version: the probability of no match is approximately exp of minus n(n-1)/(2 times 365). Set that to 0.5, so n squared over 730 equals ln 2, giving n about 22.5. Round up to 23.
   3. The pair-counting intuition is the answer to why. n choose 2 grows quadratically, so the number of chances grows fast while your intuition tracks n linearly.
   4. Contrast with the question people confuse it with: for someone to share your specific birthday you need about 253 people, because now you have only n pairs, not n squared over 2.
   5. Where this bites in real work: hash collisions and the birthday attack follow the same square-root law, and so does the chance that two of your supposedly independent signals are accidentally the same trade. You need about the square root of the space to get a collision, which is far fewer than people expect.

   Where candidates lose it

   Confusing it with the probability that someone shares your birthday, which needs 253 people. Also do not just recite 23. The gradeable part is the pair-counting argument and the exp of minus n squared over 730 approximation, which lets you answer variants like how many for a 99 percent chance without a calculator.

   Expect next

   • How many for a 99 percent chance?
   • How many to share a birthday with you specifically?
   • What is the connection to hash collisions?

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.