IMC Trading Assessment 2027: Questions & Answers

Preparing for an IMC online assessment for the 2027 trading or quant recruiting cycle? IMC's first screen is broader than most: alongside timed probability and number-sense questions, applicants commonly report cognitive games, logical reasoning tests, a values questionnaire, and a recorded video interview. Below are twelve original practice questions with complete solutions, a guide to each reported component, and a two-week preparation plan.

Your preparation priorities: fast and accurate arithmetic, probability with explicit assumptions, expected value turned into a decision, pattern and logic puzzles under a clock, and a clear account of why you want to trade. Work through the foundations first, then the four harder problems. All exercises below are original Quant Blueprint practice material.

Start with the right role and instructions

IMC hires graduates and interns into trading, quantitative research, and technology, and every graduate hire joins a structured traineeship with its own school for each track. Its students and graduates page says the process kicks off with an online assessment so that only suitable candidates are invited to interview, and its recruitment process page describes the assessment as role dependent. Build your preparation around the role you actually applied to.

Before starting an assessment, check:

• Role: trader, quant researcher, or software engineer. A coding screen on HackerRank and a probability screen need different weeks of preparation.
• Components: how many separate tests your invitation lists, whether a video interview is included, and whether each part has its own deadline.
• Rules: calculator use, scratch paper, whether you can return to earlier questions, and whether the test is adaptive.
• Environment: a quiet room, a stable connection, and a device the test platform supports. Cognitive games in particular punish a laggy browser.
• Adjustments: contact the recruiting team before the deadline if you need an accommodation or clarification.

For wider context, see the IMC career guide. If you want to find your weakest topic first, use our free quant interview diagnostic.

What the IMC assessment contains

Train for a short quantitative screen and for cognitive and personality tests that cannot be crammed. IMC does not publish a question count or time limit. Commonly reported formats give you useful practice benchmarks:

Use your invitation to choose the final rehearsal format. Test composition varies by role, region, and year. The table describes what candidates report, not an official specification, so check the components and time limits listed in your own email before deciding how to split your time.

For a 15-question, 30-minute practice screen the average budget is 2 minutes per question. Bank time on the arithmetic and number-sense items so that a geometric probability or a decision-tree question can take four or five minutes without costing you the end of the test.

Eight original IMC-style practice questions

Write down your answer before expanding each solution. Begin untimed. Once you can explain the method reliably, repeat similar problems with a timer.

1. Mental math: 72 × 68

Question: Calculate 72 × 68 without a calculator.

Show answer and explanation

Answer: 4,896. Write the factors as 70 + 2 and 70 − 2. Their product is 70² − 2² = 4,900 − 4 = 4,896.

Why this helps: IMC's screen and its later rounds both reward recognizing structure before multiplying. A second check is 72 × 70 − 72 × 2 = 5,040 − 144. When training, record whether a mistake came from the method or the arithmetic.

Try next: 2.5% of 640. Since 2.5% is 1/40, the answer is 16.

2. Percentage change has two bases

Question: A stock rises from $80 to $92. What is the percentage gain? If it then falls back to $80, what is the percentage loss?

Show answer and explanation

Answer: a 15% gain, then a loss of about 13.0%. The gain is 12/80 = 0.15. The loss uses the new base: 12/92 ≈ 0.1304.

Common mistake: assuming the round trip is +15% then −15%. Percentage changes in opposite directions never cancel unless the bases match. In general the factors multiply: 1.15 × (80/92) = 1.

Follow-up: after a 25% loss, the gain needed to recover is 1/0.75 − 1 ≈ 33.3%.

3. Sequences: state the rule you chose

Question: Find a simple rule for 3, 5, 9, 17, 33 and predict the next value.

Show answer and explanation

Answer: 65 under the rule 2ⁿ + 1. The differences are 2, 4, 8, 16, so the next difference is 32. Equivalently, each term is double the previous term minus one: 2 × 33 − 1 = 65.

Common mistake: treating a finite sequence as having one mathematically unique continuation. Several rules fit five observations. In a timed reasoning test, find the simplest rule, check it against every given term, and move on.

4. Deduction: who is telling the truth?

Question: Three traders each make one statement. A says "B is lying." B says "C is lying." C says "A and B are both lying." Each statement is entirely true or entirely false. Who is telling the truth?

Show answer and explanation

Answer: only B. Suppose C is truthful. Then A and B are both lying. But if A is lying, B is not lying, which contradicts B lying. So C is lying. C lying means A and B are not both lying, so at least one of them is truthful. B says C is lying, which we have just shown, so B is truthful. A says B is lying, which is false, so A is lying.

Method: assume one statement and follow its consequences until you reach a contradiction or a consistent assignment. Logical reasoning tests reward writing the chain down rather than holding it in your head.

5. Geometric probability in a square

Question: A point is chosen uniformly at random inside a square of side 2. What is the probability it lies within distance 1 of the center?

Show answer and explanation

Answer: π/4, about 0.785. The disc of radius 1 around the center fits entirely inside the square, so the probability is the ratio of areas: π × 1² / 2² = π/4.

Follow-up: the probability of lying within distance 1 of a chosen corner is a quarter disc over the square: (π/4) / 4 = π/16, about 0.196. Always confirm that the region you are measuring stays inside the sample space before dividing areas.

6. Bayes with a rare event

Question: One percent of orders are erroneous. A monitor flags 95% of erroneous orders and also flags 10% of correct orders. An order is flagged. What is the probability it is erroneous?

Show answer and explanation

Answer: about 8.8%. The erroneous-and-flagged branch has probability 0.01 × 0.95 = 0.0095. The correct-and-flagged branch has probability 0.99 × 0.10 = 0.099. Divide the branch of interest by all flagged branches: 0.0095 / 0.1085 ≈ 0.0876.

Why the answer feels low: the false-positive branch dominates because correct orders are 99 times more common than erroneous ones. A high detection rate on a rare event does not make a flag reliable. A useful sanity check is to imagine 1,000 orders: about 9.5 true flags against about 99 false ones.

7. Fair value and the decision that follows

Question: A coin lands heads with probability 0.6. A contract pays $10 on heads and nothing on tails. What is its fair value? Would you buy it at $5.50? At $7.00?

Show answer and explanation

Answer: fair value $6. Buy at $5.50; do not buy at $7.00. Expected payout is 0.6 × $10 = $6. Buying at $5.50 has expected profit of $0.50 per contract; buying at $7.00 loses $1.00 in expectation.

Explain the limit: if you were unsure whether the coin was 60% or 50% heads, with equal prior weight, fair value would drop to $5.50 and the $5.50 offer becomes a zero-edge trade. Then ask why the seller is happy at that price. Market-making questions at IMC are testing whether you connect a probability to a price and then ask what the other side knows.

8. Counting codes

Question: How many four-digit codes have strictly increasing digits? A leading zero is allowed, so 0125 counts.

Show answer and explanation

Answer: 210. Any choice of four distinct digits from 0 to 9 can be arranged in increasing order in exactly one way, so count the choices: C(10, 4) = 10 × 9 × 8 × 7 / (4 × 3 × 2 × 1) = 210.

Follow-up: if the digits must be non-decreasing, so repeats such as 1133 are allowed, the count becomes C(13, 4) = 715 by the stars-and-bars argument. Recognising that ordering is forced is what turns an intimidating count into a single binomial coefficient.

Four harder problems for the quantitative screen

These original examples extend the foundations into recurrences, continuous probability, options basics, and the value of information. Write the model before the calculation.

9. Waiting for two sixes in a row

Question: You roll a fair six-sided die repeatedly. What is the expected number of rolls until you see two sixes in a row?

Show answer and explanation

Answer: 42 rolls. Let E be the expected rolls from scratch and F the expected further rolls when the previous roll was a six. From scratch, one roll either gives a six (probability 1/6) or resets: E = 1 + F/6 + 5E/6, so E = 6 + F. After a six, one more roll either finishes or resets: F = 1 + 5E/6. Substituting gives E = 7 + 5E/6, so E/6 = 7 and E = 42.

Check: the expected wait for a single six is 6, and requiring an immediate repeat multiplies the wait by more than 6 because a failed repeat throws away the first six too. For a pattern of k consecutive sixes the answer is (6ᵏ⁺¹ − 6) / 5, which gives 6, 42, 258.

10. Two uniforms and a region

Question: X and Y are independent, each uniform between zero and one. What is the probability that X + Y is less than 1/2? What is the probability that |X − Y| is less than 1/4?

Show answer and explanation

Answer: 1/8 and 7/16. Draw the unit square. The region X + Y < 1/2 is a right triangle with legs 1/2, so its area is 1/2 × 1/2 × 1/2 = 1/8. The region |X − Y| < 1/4 is a band around the diagonal. Its complement is two triangles with legs 3/4, total area (3/4)² = 9/16, so the band has area 7/16.

Method: for two independent uniforms, every probability question is an area question. Sketch first, then compute. This is the same skill as question five in a different costume.

11. Put-call parity without a formula sheet

Question: A stock trades at $100. Ignore interest and dividends. A call with strike $100 trades at $4. What is the fair price of the $100-strike put? If a call with strike $105 trades at $2, what is the fair price of the $105-strike put?

Show answer and explanation

Answer: $4 and $7. Owning a call and selling a put at the same strike replicates a forward on the stock at that strike. With no interest or dividends, call minus put equals stock minus strike: C − P = S − K. At K = 100, P = 4 − (100 − 100) = 4. At K = 105, P = 2 − (100 − 105) = 7.

What to explain: the $105 put is worth more than the $105 call because the put is in the money by $5, and the two prices share the same $2 of time value. IMC's roots are in options market making, so being able to draw the payoff at expiry and reason about parity is worth more than reciting a pricing formula. State the assumptions you dropped: interest, dividends, and early exercise.

12. How much is a peek worth?

Question: A ticket pays $10 if the sum of two fair dice is at least 10. It is offered at its fair value. Before deciding whether to buy, you can pay to see the first die. What is the most a risk-neutral player should pay for that peek?

Show answer and explanation

Answer: $5/6, about $0.83. Without the peek, six of the 36 ordered outcomes have a sum of at least 10, so fair value is $10 × 6/36 = $5/3 and the trade has zero expected profit. With the peek you buy only when the conditional value exceeds the price. A first die of 1, 2, or 3 makes the payout impossible. A 4 gives a conditional value of $10 × 1/6, equal to the price, so no gain. A 5 gives $10 × 2/6, a gain of $10/6. A 6 gives $10 × 3/6, a gain of $20/6. Averaging over the six equally likely first rolls: (0 + 0 + 0 + 0 + 10/6 + 20/6) / 6 = 5/6.

Why this matters: information is worth exactly the improvement in the decision it lets you make, never more. This is the structure behind the decision-tree and information questions candidates report on the IMC screen, and behind a large part of trading.

For questions candidates have actually reported from IMC interviews, including the horse-racing puzzle, the robot on a table, and payoff diagrams, see the IMC interview question bank.

The cognitive tests, the questionnaire, and the video interview

The quantitative screen is the part you can drill. The other components reward preparation of a different kind.

Cognitive games and reasoning tests. Candidates report game-style tasks measuring working memory, attention, and pattern recognition, alongside numerical and logical reasoning tests. You cannot memorize your way through these, but you can remove avoidable losses: read every instruction screen fully, do the practice round when one is offered, sit the test rested and at a time of day you think clearly, and use a wired connection on a laptop rather than a phone. Timed sequence and deduction puzzles, like questions three and four above, are the closest thing to a warm-up.

Values and mindset questionnaire. Forced-choice personality items ask you to rank statements that all sound reasonable. Answer honestly and consistently. Trying to reverse-engineer an ideal profile produces contradictions that are easier to detect than an unusual but coherent one. IMC's own interview preparation article says it looks for a passion for solving quantitative problems, resilience in the face of uncertainty, humility, a collaborative spirit, and interests outside academics.

Recorded video interview. Prepare one example each of making a decision with incomplete information, changing your mind after new evidence, recovering from a setback, and improving a team result. Describe what you actually did, in about two minutes, and practice aloud with a timer. IMC's article warns against sounding rehearsed, so aim for notes you can talk from rather than a script you read. Connect your interest in trading to something specific you have done, whether a trading competition, a research project, or a market you follow closely.

A two-week IMC preparation plan

Use this as a starting schedule and move time toward the topics your error log identifies. If your deadline is closer, prioritize the diagnostic, core probability, and the video answers rather than trying to cover everything.

A useful error log distinguishes concept, setup, arithmetic, and time management. If you repeatedly mishandle the base of a percentage change, faster arithmetic will not fix the problem. If your model is sound but you copy numbers incorrectly, work on execution before adding harder questions.

Common questions

What is the IMC assessment passing score?

Set a 90% accuracy target on mixed practice before pushing for speed. IMC does not publish a passing score, and the cognitive and personality components are scored against profiles rather than a percentage. The 90% target is our training benchmark for the quantitative screen. Start untimed, fix your recurring mistakes, then reduce the time budget while keeping accuracy high.

Is the IMC assessment the same for trading, quant research, and software roles?

Prepare for the role you applied to. Trader applicants report a probability and number-sense screen plus cognitive tests and a video interview. Quant research applicants report a heavier weighting toward statistics: variance, conditional expectation, and Bayes. Software applicants report a two-problem coding screen. The questions in this guide build the trading and quantitative reasoning foundation.

Can I practice the cognitive games?

Not the exact games, and you should not need to. They measure general abilities rather than knowledge. What you can control is the conditions: rest, a quiet room, a reliable device, and full attention to the instructions. Timed puzzle practice helps you stay calm when the format is unfamiliar, which is most of the battle.

What should I study after this guide?

First, redo every question you missed without looking at the solution. Then solve its follow-up. You have learned the method when you can handle the variation, not just repeat the answer.

Next, take the eight-question diagnostic and use your weakest topics to build a four-week study plan. If you have other market makers in your pipeline, the SIG practice guide and the Optiver practice guide each add another set of worked problems. Keep a written error log throughout: the repeated mistake is the next thing to fix.

Prepare with a plan and feedback

Knowing an answer is only the beginning. You need to choose the right approach quickly, explain it clearly, and adapt when the interviewer changes the question.

Quant Blueprint's interview preparation program brings together technical lessons, a question bank, mock interviews, and individual feedback. Work through the concepts, practice explaining your reasoning, and use the feedback to focus your next session.

Book a free session to learn how the program works. See the preparation process, understand the support available, and decide whether it fits your target roles and interview timeline. You can also read student experiences.

Further reading: IMC students and graduates, IMC recruitment process, and how to prepare for an interview at IMC. Original practice exercises and study guidance by Quant Blueprint; published September 28, 2026.