<style> .math-block { margin: 1.5em 0; text-align: center; } .math-block mjx-container { max-width: 100% !important; overflow-x: hidden !important; } .math-block mjx-container svg { max-width: 100%; height: auto; } /* Quiz styling */ .quiz-block { background: #f8f9fa; border: 1px solid #e2e6ea; border-radius: 8px; padding: 24px 28px; margin: 28px 0; } .quiz-block h4 { margin-top: 0; } .quiz-options { list-style: none; padding: 0; margin: 16px 0; } .quiz-options > div { padding: 12px 16px; margin: 8px 0; border: 1px solid #d0d7de; border-radius: 6px; cursor: pointer; transition: background 0.15s, border-color 0.15s; color: #333 !important; } .quiz-options > div * { color: #333 !important; } .quiz-options > div:hover { background: #ebf2fa; border-color: #2563eb; color: #333 !important; } .quiz-options > div.selected-correct, .quiz-options > div.selected-correct * { background: #dcfce7; border-color: #22c55e; cursor: default; color: #333 !important; } .quiz-options > div.selected-wrong, .quiz-options > div.selected-wrong * { background: #fee2e2; border-color: #ef4444; cursor: default; color: #333 !important; } .quiz-options > div.reveal-correct, .quiz-options > div.reveal-correct * { background: #dcfce7; border-color: #22c55e; color: #333 !important; } .quiz-options > div.disabled, .quiz-options > div.disabled * { cursor: default; opacity: 0.7; color: #333 !important; } .quiz-block, .quiz-block * { color: #333 !important; } .quiz-explanation, .quiz-explanation * { color: #333 !important; } .quiz-explanation { display: none; margin-top: 16px; padding: 16px 20px; background: #fff; border-left: 3px solid #2563eb; border-radius: 0 6px 6px 0; } .quiz-explanation.visible { display: block; } /* References */ .ref-list { list-style: none; padding: 0; margin: 0; } .ref-list li { padding-left: 2.5em; text-indent: -2.5em; margin-bottom: 0.8em; } /* Nuclear option: force black text everywhere in quiz */ [class*="quiz"] { color: #333 !important; } [class*="quiz"] * { color: #333 !important; } [class*="quiz"] *:hover { color: #333 !important; } [class*="quiz"] li { color: #333 !important; } [class*="quiz"] li:hover { color: #333 !important; } [class*="quiz"] li:active { color: #333 !important; } [class*="quiz"] li:focus { color: #333 !important; } [class*="quiz"] li sup { color: #333 !important; } [class*="quiz"] li sub { color: #333 !important; } .quiz-options > div:hover * { color: #333 !important; } </style> <p>The phrase "quant interview" has a strange ability to make even very capable people nervous. Not because the questions are always impossibly difficult. Often, they are not. The harder part is that the questions move.</p> <p>You may begin with probability, then be asked to justify an assumption. You may write a coding solution, then be asked whether it is efficient. You may estimate a number, then receive new information that forces you to update your answer. The real test is not simply: do you know this? It is: can you use what you know when the problem doesn't stay still?</p> <p>People often imagine quantitative finance interviews as intellectual ambushes. Either you are born brilliant enough to solve everything instantly, or you are not. Dramatic, certainly. Accurate, thankfully, no. A better version is this: knowledge is learned, but thinking is trained.</p> <p>Of course, knowledge still matters. Probability matters. Statistics matter. Programming matters. Mathematical fluency matters. But knowledge alone is not the whole game. In a quant interview, the interviewer is also watching how you think: how you begin, what assumptions you make, whether you explain them, how clearly you structure your reasoning, and whether your answer can survive the next question.</p> <p>This is where many candidates make a surprisingly costly mistake: they use technical words because the words sound impressive. In a quant interview, your words can be used against you, politely, of course. If you say "Bayes' law," know why it applies. If you say an algorithm is "efficient," know whether you mean speed, memory usage, or scalability. The point is not to sound technical. The point is to think technically.</p> <p>Dirk Bester's <em>An Interview Primer for Quantitative Finance</em> treats interviewing as a skill that can be practised. His comparison is simple: you would not expect to lift 200kg without training, so you should not expect to perform well in difficult interviews without preparing for their particular shape. Bester also notes that understanding the intent of a question and communicating your reasoning are as important as reaching the final answer.</p> <p>That is what you need to train: not just answers, but structure. Pause. Clarify. Translate. Simplify. Calculate. Explain. Question. Adjust. That sequence matters.</p> <h3>Preparing for the Company, Not Just the Interview</h3> <p>One useful detail is often overlooked: you are not only preparing for a quant interview. You are preparing for a particular firm's style of thinking. The core skills overlap, but the emphasis changes depending on who is sitting across from you.</p> <p>Jane Street, for example, states that a finance background is optional and that candidates are not tested on economics. Their focus is collaborative problem-solving. They explicitly value candidates who ask strong questions, not just candidates who rush toward answers.</p> <p>Citadel Securities places emphasis on intellectual honesty, technical depth, and the ability to explain your approach. A correct number with a foggy explanation is less impressive than a clear method that can be tested, challenged, and improved.</p> <p>Optiver often emphasises probabilistic intuition and speed. Their campus material notes that prior industry knowledge is not required because their training is designed to build that foundation in people who can think clearly under pressure. In other words, they are not only asking whether you know the material. They are asking whether your mind stays organised when time is limited.</p> <p>Two Sigma looks closely at scientific thinking. They do not necessarily expect a perfect first answer. They want to see candidates build an initial solution, identify weaknesses, and improve it through careful reasoning. The perfect first answer is not always the point. The ability to iterate intelligently often matters more.</p> <p>IMC Trading, meanwhile, places strong value on accuracy and risk awareness. In trading, a fast wrong answer is not a harmless mistake. It can be a serious failure of judgment. Their process therefore rewards candidates who stay calm, precise, and adaptable.</p> <p>So the point is not that finance knowledge does not matter. It does. The point is that firms often care just as much, or even more, about what happens underneath the answer: your assumptions, your communication, your ability to update, and whether your confidence is supported by actual understanding.</p> <p>Different firms may press different buttons. But the underlying question is similar: Can you think clearly?</p> <h3>Now It's Your Turn</h3> <p>Enough theory. Let's test the idea. The point of these questions is to notice how you think. Try not to Google. Otherwise, where is the fun?</p> <!-- ═══════════════════════════ --> <!-- QUIZ 1: Probability --> <!-- ═══════════════════════════ --> <div class="quiz-block" id="quiz1"> <h4>1. The Ambiguity Test: Probability</h4> <p>You roll two fair dice. What is the probability that one die is larger than the other?</p> <div class="quiz-options" data-correct="2" data-quiz="1"> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="0"><span style="color:#333!important">A. 5/6</span></div> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="1"><span style="color:#333!important">B. 5/12</span></div> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="2"><span style="color:#333!important">C. "I have a question before I calculate anything."</span></div> </div> <div class="quiz-explanation" id="explain1"> <p>If you picked C, you are thinking like a strong quant candidate.</p> <p>Why? Because the question is ambiguous.</p> <p>If it asks for the probability that the two dice show different numbers, then one die must be larger than the other whenever they are not equal. There are 36 possible outcomes from rolling two dice. Six of them are doubles: (1,1), (2,2), and so on. That leaves 30 outcomes where one die is larger than the other. So the probability is:</p> <div class="math-block"><span style="font-size:1.3em;color:#333 !important;">30/36 = 5/6</span></div> <p>But if the question means, "What is the probability that Die A is larger than Die B?", then only half of those 30 unequal outcomes count. The other half are cases where Die B is larger. So the answer becomes:</p> <div class="math-block"><span style="font-size:1.3em;color:#333 !important;">15/36 = 5/12</span></div> <p>The lesson is simple: before solving a problem, make sure you are solving the right problem. In quant interviews, clarification is not a delay. It is part of the solution.</p> </div> </div> <!-- ═══════════════════════════ --> <!-- QUIZ 2: Statistics --> <!-- ═══════════════════════════ --> <div class="quiz-block" id="quiz2"> <h4>2. The Base-Rate Fallacy: Statistics</h4> <p>A disease affects 1% of people. A test correctly identifies 80% of people who have the disease, but it also gives a false positive result to 10% of healthy people. You test positive. What is the chance you actually have the disease?</p> <div class="quiz-options" data-correct="2" data-quiz="2"> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="0"><span style="color:#333!important">A. Around 80%</span></div> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="1"><span style="color:#333!important">B. Around 50%</span></div> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="2"><span style="color:#333!important">C. Around 8%</span></div> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="3"><span style="color:#333!important">D. Around 1%</span></div> </div> <div class="quiz-explanation" id="explain2"> <p>Most people are tempted by 80%. The test sounds reliable, and a positive result sounds alarming. But the disease is rare, and rarity matters.</p> <p>Imagine 1,000 people. Around 10 have the disease. If the test catches 80% of them, it correctly identifies 8 sick people.</p> <p>Now look at the 990 healthy people. If 10% of them receive a false positive, that creates 99 healthy people who also test positive.</p> <p>So among everyone who tests positive, there are 8 true positives and 99 false positives. That means the chance of actually having the disease is:</p> <div class="math-block"><span style="font-size:1.3em;color:#333 !important;">8/(8 + 99) = 8/107 ≈ 7.5%</span></div> <p>This is an example of Bayes' law, a way of updating probabilities when new information arrives. The important idea is not the formula itself, but the habit behind it: new evidence must be interpreted in context. A positive test means something very different when the condition is common than when it is rare.</p> </div> </div> <!-- ═══════════════════════════ --> <!-- QUIZ 3: Betting --> <!-- ═══════════════════════════ --> <div class="quiz-block" id="quiz3"> <h4>3. The Expected Value Trap: Betting</h4> <p>You flip 100 fair coins. If 60 or more land heads, you win £10. Otherwise, you win nothing. Should you pay £1 to play?</p> <div class="quiz-options" data-correct="1" data-quiz="3"> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="0"><span style="color:#333!important">A. Yes, 60 heads is a reasonable outcome.</span></div> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="1"><span style="color:#333!important">B. No, the expected value is negative.</span></div> <div style="color:#333 !important;" onmouseover="this.style.color='#333'" onmouseout="this.style.color='#333'" onclick="(function(el){var ul=el.parentElement;var correct=parseInt(ul.getAttribute('data-correct'));var idx=parseInt(el.getAttribute('data-index'));var items=ul.querySelectorAll('[data-index]');var quizId=ul.getAttribute('data-quiz');if(items[0].classList.contains('disabled'))return;for(var i=0;i<items.length;i++){items[i].classList.add('disabled');if(parseInt(items[i].getAttribute('data-index'))===correct){items[i].classList.add('reveal-correct');}}if(idx===correct){el.classList.remove('reveal-correct');el.classList.add('selected-correct');}else{el.classList.add('selected-wrong');}var exp=document.getElementById('explain'+quizId);if(exp)exp.classList.add('visible');if(window.MathJax&&MathJax.typesetPromise)MathJax.typesetPromise();})(this)" data-index="2"><span style="color:#333!important">C. No, unless I am a billionaire who gets unusual joy from bad bets.</span></div> </div> <div class="quiz-explanation" id="explain3"> <p>The answer is B.</p> <p>This is a question about expected value: the average result you would get if you could play the same game many times. A fair coin flipped 100 times has an average of 50 heads. The standard deviation, a measure of how much results typically vary, is 5. Getting 60 heads is therefore two standard deviations above the average.</p> <p>Using the normal approximation, the chance of getting at least 60 heads is only around 2.5%. That means your expected winnings are roughly:</p> <div class="math-block"><span style="font-size:1.3em;color:#333 !important;">0.025 × £10 = £0.25</span></div> <p>So you are paying £1 for something worth about 25p on average. That is not a bargain. It is a small machine for converting confidence into regret.</p> <p>The deeper lesson is that "possible" is not the same as "profitable." Many bad trades are built on outcomes that can happen. Quantitative thinking asks a sharper question: how often do they happen, and what are they worth?</p> </div> </div> <!-- ═══════════════════════════ --> <!-- QUIZ 4: Open-ended --> <!-- ═══════════════════════════ --> <div class="quiz-block" id="quiz4"> <h4>4. The Judgment Test: Making a Market</h4> <p>Now for a different kind of question:</p> <p><em>"Make me a market on the weight of the Empire State Building."</em></p> <p>This is not about knowing the exact weight of the Empire State Building. Almost nobody casually carries that number around, and if they do, they may need more hobbies. The point is to make a reasonable estimate and show how confident you are.</p> <p>In trading, to "make a market" means giving two prices: one where you would be willing to buy, and one where you would be willing to sell. Here, you are not quoting a stock. You are quoting a range for the building's weight. So your answer might look something like: "I think it is between X and Y tonnes."</p> <p>The exact numbers matter less than your reasoning. How did you think about the size of the building? What assumptions did you make? How wide is your range, and why?</p> <p>That last part is important. If you are unsure, your range should be wide. If you feel more confident, it can be narrower. In quant interviews, uncertainty is not something to hide. It is something to price.</p> <p>So try it: make a market on the weight of the Empire State Building, and explain your reasoning in a few lines. If you're a member, we're going to provide you with feedback.</p> <p>If you'd like to send us your answer, email us at <a href="mailto:contact@amsquants.nl" style="color:#2563eb !important;">contact@amsquants.nl</a>!</p> </div> <h3>What These Questions Are Testing</h3> <p>As you probably noticed, these questions test different things. The first three are more structured: once you understand the setup, there is a clean mathematical answer. The fourth is broader. It gives you more freedom, but also asks more from your reasoning.</p> <p>And that is the point. Quant interviews vary by firm, but the foundation is similar: clear thinking, good assumptions, careful communication, and the ability to update your answer when the problem changes.</p> <p>So preparation should be about quality before quantity. Doing hundreds of questions is not very useful if you never stop to ask: Did I understand the question? What am I assuming? Does my answer actually make sense? Could I explain it simply and structurally?</p> <p>The questions may change, but the underlying skills do not change that much. That is why older books, classic problems, and past preparation materials can still be extremely useful. You are not just collecting answers, you are mostly training your own way of thinking.</p> <p>If you want a list of books and resources for preparing for quant interviews, leave a comment and we'll share it with you.</p> <h3>Sources Cited</h3> <style> .sources-list { list-style: none; padding: 0; margin: 0; } .sources-list li { padding-left: 0; margin-bottom: 0.6em; font-size: 0.95em; } </style> <ul class="sources-list"> <li>Akuna Capital. (2024). <em>Akuna Interview Guide & Mental Math Assessment</em>. Official Career Resource.</li> <li>Bester, D. (2019). <em>An Interview Primer for Quantitative Finance</em>. V1.2.0.</li> <li>Citadel Securities. (2024). <em>Quantitative Research: The Interview Process and Preparation</em>. Official Career Portal.</li> <li>IMC Trading. (2024). <em>Graduate & Internship Careers: Accuracy and Risk Management</em>. IMC Official Website.</li> <li>Jane Street. (2025). <em>Interviewing at Jane Street: Quantitative Trading & Strategy</em>. Official Career Guide.</li> <li>Optiver. (2024). <em>Campus Recruitment: Graduate Trading and Quantitative Research Foundations</em>. Optiver Official Website.</li> <li>SIG (Susquehanna International Group). (2024). <em>Game Theory and Decision Science in Trading</em>. SIG Careers.</li> <li>Two Sigma. (2024). <em>The Scientific Method in Finance: How We Interview</em>. Two Sigma Official Blog.</li> </div>
