Citadel-Style Dual Online Assessment

How it works

The sitting runs two sections in order, about 42 minutes in total. The first is the Cognitive screen: 50 items in 12 minutes, roughly 14 seconds each, mixing arithmetic (round-number shortcuts, percentage swaps, clean divisions, and similar mental-math items) with logic and verbal items - syllogism-style deduction, odd-one-out categorization, alphabet skip-count letter series, and short two-sentence comprehension questions - built from roughly half arithmetic and half logic/verbal, shuffled together.

The second section is the Probability OA: 15 items in 30 minutes, about two minutes each, covering an extended Bayes update on stones drawn from a bag, the long-run stationary distribution of a two-state Markov chain, the expected number of steps for a random walk to hit an absorbing boundary, a combinatorics question with a paired constraint, an optimal-stopping card-calling question, the variance of a binomial count, the concept behind a one-sample t-statistic, a conditional-expectation question, the coupon collector's expected number of trials, and a procedure question about generating a uniform range from an unfair number of die faces.

Neither section penalizes a wrong answer, and neither allows going back once an item is left - you answer or skip, and the next item loads. The two sections have very different rhythms: the cognitive screen rewards raw speed since there is barely enough time to read each item once, while the probability OA gives enough time per item that a rushed answer is more often a reasoning error than a time-pressure one.

How scoring works

Both sections use penalty 0, so each section's raw score is simply its count of correct answers - a wrong answer scores the same as a blank. The sitting's overall scaled score is the sum of the two sections' raw scores, out of a maxScaled of 65 (50 + 15). The review screen reports this as a percentage: round(scaled / 65 x 100).

Both sections have allowBack set to false, so once you leave an item in either section you cannot return to it. Flagging an item during the run marks it for the final review screen only - it has no effect on navigation within the timed sections, since neither permits jumping back regardless of the flag.

The review screen surfaces every flagged item, across both sections, with the prompt, what you entered, the correct answer, and the explanation, once the entire sitting - both sections - has finished.

Cognitive screen

At roughly 14 seconds an item, this section is slightly less rushed per-question than a headline mental-math round but still leaves no time for a full derivation. For the arithmetic half, the same shortcuts apply as any speed-arithmetic test: look for round-number pairs, percentage swaps, and clean divisions before doing the arithmetic longhand.

For the logic and verbal half, the key discipline is testing each answer choice directly against the given premises rather than reasoning it through purely in your head. A syllogism item is built so several choices are merely plausible rather than logically forced - the only correct answer is the one that must be true given exactly the stated premises, no more and no less. The same applies to the short comprehension items: a passage stating a stock halts at a 10% move within five minutes, followed by two moves that sum past that threshold within the window, has exactly one entailed conclusion, and the wrong choices are built to look almost as reasonable.

For letter series and odd-one-out items, identify the underlying rule explicitly - a skip-count spacing through the alphabet, or a shared property like all-perfect-squares or all-prime - rather than pattern-matching by eye, since the wrong choices are chosen to be close neighbors of the right answer.

Probability OA

With about two minutes per item, there is real time to set a problem up correctly, and doing so is worth more here than in the faster cognitive screen. The Bayes-style stones question is the one most likely to be answered too quickly: after observing two black draws with replacement, the posterior over how many stones in the bag are black shifts toward black-heavy compositions, so the probability the next draw is also black is not simply the naive count-over-total - it requires weighting each possible composition by how well it explains the two draws already observed.

For the Markov chain items, get the stationary-distribution balance equation direction right: in the long run, the flow from Calm to Volatile must equal the flow back, so pi(Calm) times the Calm-to-Volatile probability equals pi(Volatile) times the Volatile-to-Calm probability - solving that balance, not the raw transition probabilities themselves, gives the long-run fraction of Calm days. The absorbing-boundary random walk question has a clean closed form worth memorizing: starting at position i on a line from 0 to N with both ends absorbing, the expected number of steps to absorption is i times (N minus i).

For the combinatorics-with-constraint item, fix whatever is constrained first (for example, both siblings placed on the team) and count the remaining choices from what's left, rather than counting all arrangements and trying to filter afterward. The hypothesis-testing item tests a single concept: dividing a sample mean by its standard error (s over the square root of n), not by the raw sample standard deviation alone, is what makes a statistic sharpen correctly as more data arrives.

Pacing across the whole sitting

The two sections demand almost opposite modes of thinking - fast pattern-matching for 12 minutes, then slower, careful setup for 30 - and the biggest pacing risk is carrying the first section's urgency into the second, where a two-minute Markov or Bayes question genuinely benefits from writing the setup down before computing anything.

Since neither section penalizes a wrong answer, never leave an item blank purely because time is short in either section - a fast, partially-reasoned guess (ruling out one or two clearly wrong choices, or estimating the right order of magnitude) always beats a skip.

A worked example

1. Setup: a token starts at position 1 on the line 0-1-2-3-4, moving left or right with probability 1/2 each step, and positions 0 and 4 absorb it.

   $$N = 4, \qquad \text{start position } i = 1$$

2. The expected number of steps to absorption from position i on a line of length N with both ends absorbing has a closed form.

   $$E[\text{steps} \mid X_0 = i] = i(N - i)$$

3. Plug in the given start position and boundary.

   $$E[\text{steps}] = 1 \times (4 - 1) = 3$$

4. Sanity check the formula against every position on this line: it should be smallest near the edges, where absorption happens fast, and largest at the center.

   $$i(N-i):\ \ 1\cdot 3 = 3,\quad 2\cdot 2 = 4,\quad 3\cdot 1 = 3$$

5. Position 1 gives the smallest of the interior values, consistent with starting one step from an absorbing boundary. Enter 3.

Common mistakes

• On the cognitive screen, trying to fully prove a syllogism instead of testing each answer choice directly against the two given premises - there is no time at 14 seconds a question for a formal derivation.

• Confusing "must be true" with "could be true" on syllogism and comprehension items. These items are built so several choices are merely consistent with the premises, not logically forced by them, and only the forced conclusion is correct.

• On the stones-in-a-bag Bayes item, treating the two observed draws as independent of the bag's unknown composition - two black draws in a row shift the posterior toward black-heavy compositions, so the next-draw probability isn't simply a naive count over total.

• Setting up the Markov stationary-distribution balance equation backwards - it balances the flow between states (probability in a state times its transition rate out), not the states' raw transition probabilities against each other directly.

• Leaving Probability OA items blank because two minutes still feels tight. Neither section penalizes a wrong answer, so any answer, including a partially-reasoned guess, is strictly better than a skip.

Why interviews test this

Splitting a hire's screening into a fast general-aptitude stage and a slower role-specific stage mirrors how large quantitative firms are widely reported to actually run their pipelines: a broad, cheap-to-grade filter first, reserving deeper and more expensive-to-design content for candidates already confirmed to clear a speed and reasoning bar. The two stages test genuinely different things, which is why both survive in the pipeline rather than one being redundant with the other.

The cognitive screen is meant to filter for raw processing speed and careful reading under pressure, independent of finance background - a candidate who can't reliably tell a forced conclusion from a merely plausible one in 14 seconds is unlikely to keep pace with fast-moving information later. The probability OA is meant to filter for something else entirely: whether a candidate has actually internalized concepts like Bayesian updating, Markov stationarity, and the logic of a hypothesis test well enough to apply them correctly to an unfamiliar setup in real time, rather than only being able to recite the formulas.