Got your Citadel Securities math test? Try the test below in the real format, then read what it asks, how to answer typed probability questions fast and what comes after. This page covers the Quantitative Trader internship at Citadel Securities, the market maker, which is a separate firm from Citadel, the hedge fund.
Key facts
- Format: A timed online test of math, probability and statistics: 15 questions in 30 minutes in Aug 2024 (summer 2025), and about 15 questions again in a 2025 sitting. An Aug 2022 (summer 2023) sitting ran 20 minutes.5,8,4
- Answers: In a 2025 sitting each question was fill-in: you typed the number rather than choosing from a list.8
- What it covers: Counting, probability and statistics, with logic questions in Aug 2022 (summer 2023) and coding beside them in Oct 2025 (summer 2026).4,6,7,8
- When it comes: The test link came within a week of applying in Aug 2022 (summer 2023) and Aug 2024 (summer 2025); another Aug 2024 applicant heard back within a month.4,5,6
- Coding: An Oct 2025 (summer 2026) New York sitting mixed coding questions with the probability ones.7,9
- Proctoring: The Aug 2024 (summer 2025) sitting was timed with no camera. The questions were fair; the clock was the hard part.6
- Next step: Pass and a Zoom interview of about 45 minutes follows: a short talk about your background, then probability, math and statistics problems.2,4,5
Not every process includes the test. Citadel Securities' own page on its intern process lists two phone screens and an onsite, names no test, and says the exact sequence can vary by candidate; for summer 2027, a first-round interview in Jul 2026 came with no test beforehand.9,2
Try the games
Citadel Securities's quantitative trading test on HackerRank's typed test screens, as the app draws it: one clock, free movement between questions, and every answer typed, with no options to pick from. It opens in its own window at the real pace, with a report at the end.
Quantitative Trading Assessment
15 probability and statistics questions in 30 minutes, every answer typed as a whole number or a fraction.
5 questions · 10:00
What the Citadel Securities online assessment looks like
The invite
The test link comes by email after you apply: within a week in Aug 2022 (summer 2023) and Aug 2024 (summer 2025), and within a month in another Aug 2024 process. Not every process includes it: for summer 2027, a first-round interview in Jul 2026 came with no test beforehand.4,5,6,9
The test
15 questions in 30 minutes in Aug 2024 (summer 2025), and about 15 again in a 2025 sitting, so plan on a little under 2 minutes each. In the 2025 sitting every question took a typed answer. The Aug 2024 sitting ran with no camera, and the questions were manageable; the clock was the pressure. Older sittings split 10 probability questions into four separately timed sections, so read the instructions screen before you start.5,6,8
What it asks
Counting, probability and logic in Aug 2022 (summer 2023); math and statistics in Aug 2024 (summer 2025); probability and statistics in 2025.4,6,8
Coding
The Oct 2025 (summer 2026) New York test had coding questions beside the probability ones. If your invite lists a coding part, have your strongest interview language ready: the application asked for your top two.7,9,1
After you submit
Pass and the next step is a Zoom interview of about 45 minutes with a trader: a short talk about your background, then probability, math and statistics, worked out loud. Interns generally have a second 45-minute screen, then an onsite superday in New York or Miami.2,4,5,6
Before you start the test
- Watch for the link in the week or so after you apply, and check your spam folder.
- A laptop or desktop on a stable connection, other tabs closed.
- Pen and plenty of scrap paper for sample spaces and sums.
- Practice timed sets without a calculator: about 2 minutes a question.
- Refresh counting, conditional probability, expected value and variance.
- Your strongest coding language warmed up, in case the test has a coding part.
- Phone off and 30 quiet minutes blocked, with time for the instructions first.
The sections, one by one
Citadel Securities looks for strong foundations in math, probability and statistics, and for a rigorous, statistical approach to uncertainty. The test checks exactly that, fast and by hand: set the problem up, then get the exact number.2,1,3,4,8
- Probability: Dice, coins, cards and draws from a bag, with or without replacement.
- Conditional probability: Update a chance after new information, Bayes style.
- Expected value: The fair price or average payout of a game.
- Counting: Arrangements, choices and routes, the basis of most probability answers.
- Statistics: Means, variances and covariances of simple random variables.
- Coding (some sittings): Short coding questions, beside the probability ones in Oct 2025 (summer 2026).
Here is the test as it appears in Intervyo: one paper of probability and statistics questions, a typed answer box under each one, and a report at the end with the working for every answer. The block says what the test checks and how to answer it well.5,8
1.Quantitative trading math test15 questions, 30 minutes
15 questions in 30 minutes in Aug 2024 (summer 2025), so a little under 2 minutes each. Answers were typed in a 2025 sitting: with no options to check against, a slip in the setup goes straight into the answer. The Aug 2024 (summer 2025) sitting ran with no camera, and the difficulty came from the clock, not the questions.5,6,8,3
What it measures: Exact probability under time pressure: setting up the sample space, conditioning correctly, expected values and simple variances, the risk-under-uncertainty and statistics skills Citadel Securities lists for its traders.
How to answer it well
- 1Write the sample space first: how many equally likely outcomes, and which of them count.
- 2Ask whether the draws are with or without replacement before you multiply anything.
- 3For "at least one", work out the chance of none and take it from 1.
- 4Give the answer in the form the question asks. A fraction in lowest terms is the safe default; reduce it before you type it.
- 5Variance is the mean of the squares minus the square of the mean. For a fair n-sided die it is (n^2 - 1)/12, and variances of independent rolls add.
- 6Budget about 2 minutes a question. If one stalls, type your best answer and come back to it if time is left.
Best guessPractice without a calculator, on one 30-minute clock, on HackerRank-style typed questions. Older sittings ran on HackerRank in separately timed sections, so check the instructions screen for the clock before you start.
Example items and how to approach them
Probability"Two fair six-sided dice are rolled. What is the probability that the higher of the two numbers is exactly 4? Give your answer as a fraction in its lowest terms."4,8
- 1Turn "exactly 4" into two easier counts: at most 4, minus at most 3.
- 2Count each as a square: both dice at most 4 is 4 x 4.
- 3Subtract, then divide by all 36 outcomes.
- 4Reduce the fraction before you type it.
Tip: Written by Intervyo in the test's format: one typed answer. Not a Citadel Securities item.
Example answer, written by Intervyo (not a real candidate)
Written by Intervyo as an example. Both dice at most 4: 16 outcomes. Both at most 3: 9. So the higher one is exactly 4 in 16 - 9 = 7 outcomes, and the answer is 7/36.
Drawing without replacement"Two cards are drawn from a standard 52-card deck without replacement. What is the probability that both are hearts? Give your answer as a fraction in its lowest terms."4,8
- 1Spot "without replacement": the second draw depends on the first.
- 2Multiply the chance of a heart first by the chance of a heart second, given the first was one.
- 3Cancel early so the numbers stay small.
Tip: Written by Intervyo in the test's format. Not a Citadel Securities item. Squaring 1/4 is the trap: it treats the draws as independent.
Example answer, written by Intervyo (not a real candidate)
Written by Intervyo as an example. 13/52 x 12/51 = 1/4 x 4/17 = 1/17. Squaring 1/4 would give 1/16, which is wrong because the deck has one heart fewer after the first draw.
Conditional probability"A bag holds two coins: one fair and one with heads on both sides. You pick one at random and toss it twice, and it lands heads both times. What is the probability that you picked the two-headed coin? Give your answer as a fraction in its lowest terms."8,9
- 1Write down each coin's prior: 1/2 each.
- 2Find the chance of two heads with each coin: 1 and 1/4.
- 3Weight each by its prior, then divide the two-headed share by the total.
Tip: Written by Intervyo in the test's format. Not a Citadel Securities item. Bayes questions reward a quick table of prior x likelihood.
Example answer, written by Intervyo (not a real candidate)
Written by Intervyo as an example. Two-headed: 1/2 x 1 = 1/2. Fair: 1/2 x 1/4 = 1/8. Total 5/8, so the chance it is the two-headed coin is (1/2) / (5/8) = 4/5.
Statistics"X is the total of two fair six-sided dice. What is the variance of X? Give your answer as a fraction in its lowest terms."6,8
- 1Find the variance of one die: (n^2 - 1)/12 for a fair n-sided die.
- 2The dice are independent, so the variances add.
- 3Reduce the result.
Tip: Written by Intervyo in the test's format. Not a Citadel Securities item. Knowing the one-die variance saves a full table of 36 outcomes.
Example answer, written by Intervyo (not a real candidate)
Written by Intervyo as an example. One die: (36 - 1)/12 = 35/12. Two independent dice: 2 x 35/12 = 35/6.
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How long to hear back after the online assessment
The math test sits at the start of the process, and a pass leads to a Zoom screen with a trader. The test has come within a week to a month of applying.4,5,6,2
Aug 2022 (summer 2023)
Quant trader intern, New York
The test within a week of applying: 20 minutes of counting, probability and logic. A 45-minute technical phone screen with a trader followed.4
Aug 2024 (summer 2025)
Quant trader intern, New York
Applied through a referral and got the math test a week later: 15 questions in 30 minutes, about 12 right by their own count. A phone interview with a trader followed.5
Aug 2024 (summer 2025)
Quant trading intern, New York
Heard back within a month with a timed math and statistics test, no camera. Then a phone call with a trader on the resume and expected value.6
Oct 2025 (summer 2026)
Quant trader intern, New York
A test of coding and probability questions, then two 45-minute interviews and an in-person superday.7
Jul 2026 (summer 2027)
Internship applicant
Invited to a first-round interview with no test beforehand.9
Citadel Securities asks you to tell your recruiting contact as soon as you have a competing offer or deadline, and says it will do its best to work to it.2
Best guessExpect the Zoom screen invite within one to two weeks of submitting if you pass. If three weeks go by with nothing, keep your other applications moving.
What happens after the online assessment
Online application
One shared trading form, with a resume, education history and short questions.1
Online math testYou are here
This page. A timed probability and statistics test about a week after applying: 15 questions in 30 minutes in Aug 2024 (summer 2025); coding in some sittings.4,5,7,8
Trader interviews (1 or 2)
Zoom screens of about 45 minutes: probability, math and statistics first, then trading sense, research or programming in the second.2,7
Superday
In person in New York or Miami: a desk shadow, a group trading exercise and three individual interviews.2
Offer
A decision has come about a week after the final round.9
Online math test vs the first phone screen
Both test the same probability and statistics. The test wants the exact number, fast and alone; the screen wants to hear how you get there.
Format
15 questions in 30 minutes in Aug 2024 (summer 2025); about 15 typed ones in 2025.5,8
A Zoom interview of about 45 minutes.2
Content
A short talk about your background, then probability, math and statistics problems.2
FAQ
What is on the Citadel Securities online assessment?
Math, probability and statistics: counting, probability and simple statistics, with logic questions in Aug 2022 (summer 2023). The Oct 2025 (summer 2026) New York test added coding questions.4,6,7,9
How long is the Citadel Securities math test?
15 questions in 30 minutes in Aug 2024 (summer 2025), and about 15 questions again in a 2025 sitting. An Aug 2022 (summer 2023) sitting ran 20 minutes, so check the instructions screen for your own clock.5,8,4
Is the test multiple choice?
Not in a 2025 sitting: each question took a typed answer, so practice giving the exact number. A fraction in lowest terms is the safe default unless the question asks for something else.8
Does everyone take the test?
Not always. In New York processes from 2022 to 2025 it came about a week after applying. Citadel Securities' own page on its intern process lists two phone screens and an onsite with no test and says the sequence can vary by candidate, and for summer 2027 one first-round interview in Jul 2026 came with no test beforehand.4,5,9,2
Is the Citadel Securities test proctored?
The Aug 2024 (summer 2025) sitting was timed with no camera. Treat it as one sitting you take alone, start to finish.6
Is this the same test as Citadel's?
No. Citadel Securities, the market maker, and Citadel, the hedge fund, are separate firms, though the US trading form lists roles at both. This page covers the Citadel Securities Quantitative Trader test only.1
How should I prepare for the Citadel Securities online assessment?
Refresh probability, math and statistics until you can apply them to problems you have not seen, then practice timed sets by hand at about 2 minutes a question. Intervyo's Citadel Securities practice gives a full paper of typed probability and statistics questions on one clock, with a report and the working for every answer.2,5
Online assessment at other firms
Sources
Firm pages first, then dated candidate reports. Last checked Nov 11, 2026.
- 1Citadel Securities: Quantitative Trader - Intern (US) (Trading and Research), posting and application form
- 2Citadel Securities: Quantitative Trading Interview Process (Nov 2026)
- 3Citadel Securities: Candidate FAQs: Markets & Trading
- 4Candidate report on a public forum: Quant Trader Internship interview, New York (Aug 2022)
- 5Candidate report on a public forum: Quant Trader Intern interview, New York (Aug 2024)
- 6Candidate report on a public forum: Quant Trading Intern interview, New York (Aug 2024)
- 7Candidate report on a public forum: Quant Trader Intern interview, New York (Oct 2025)
- 8QuantVault: Citadel / Citadel Securities Online Assessment: Format, Questions & Free Practice · prep site
- 9Trading Interview: Citadel Securities Internship 2027: Pay, Roles And Interview Process · prep site
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