Numerical Reasoning Tests Interview Questions for Quant Researchers
The same round is marked differently depending on the seat you are interviewing for. This is the numerical reasoning tests set as it applies to quant researchers.
132 questions, all free to practise. The split is 52 easy, 66 medium, 14 hard. The topics that come up most are probability (59), expected value (30), brainteasers (29), combinatorics (22).
- A die with one face decrementedEasyProbabilityConditional Probability & ExpectationView →
- A guest list with a feudEasyCombinatoricsView →
- A limit that hides a difference of logsEasyCalculusView →
- A mile with no windEasyBrainteasersView →
- A root of a product plus oneEasyBrainteasersView →
- A sum of four before a sum of twoEasyProbabilityView →
- A sum of three cubesEasyBrainteasersView →
- An alternating sum of squaresEasyBrainteasersView →
- An infinite nested radicalEasyBrainteasersView →
- At least one blue and one greenEasyProbabilityCombinatoricsView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Clock angle at 3:15EasyBrainteasersView →
- Coin rolling around a coinEasyBrainteasersView →
- Correlation from a summed varianceEasyRandom VariablesStatisticsView →
- Crossing the origin twiceEasyStochastic ProcessesView →
- Dots on distinct edgesEasyProbabilityCombinatoricsView →
- Expected distance of a dart from centerEasyProbabilityRandom VariablesView →
- Expected flips after a losing startEasyProbabilityExpected ValueView →
- Expected flips for three headsEasyProbabilityExpected ValueView →
- Expected flips for two heads (not in a row)EasyProbabilityExpected ValueView →
- Four dice summing to twentyEasyProbabilityCombinatoricsView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Keep the d8 or gamble on the d12?EasyProbabilityExpected ValueView →
- Lapping on the trackEasyBrainteasersView →
- Lattice paths through a checkpointEasyCombinatoricsView →
- Matching locks to keysEasyBrainteasersView →
- Normalizing a tilted densityEasyRandom VariablesCalculusView →
- One blue die matches the redEasyProbabilityView →
- Origin between two pointsEasyProbabilityView →
- Paid the last roll before you stopEasyProbabilityExpected ValueView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Ripple on a pondEasyCalculusView →
- Rolling a die to size the next dieEasyConditional Probability & ExpectationExpected ValueView →
- Rolling until you match the first rollEasyProbabilityExpected ValueView →
- Rolls until an even sumEasyProbabilityExpected ValueView →
- Same side four timesEasyProbabilityView →
- Shrinking the standard errorEasyStatisticsView →
- Tangent-minus-sine third-order limitEasyCalculusView →
- The higher die shows a fourEasyProbabilityView →
- The weight of the fishEasyBrainteasersView →
- Three primes in six rollsEasyProbabilityView →
- Timing the revolverEasyBrainteasersView →
- Top three dice summing to eighteenEasyProbabilityCombinatoricsView →
- Two mismatched diceEasyProbabilityView →
- Unchanged after ten swingsEasyProbabilityBrainteasersView →
- Variance of an asymmetric random walkEasyRandom VariablesStochastic ProcessesView →
- Ways to reach deuceEasyProbabilityCombinatoricsView →
- When the clock hands next meetEasyBrainteasersView →
- Where the maximum landsEasyRandom VariablesStatisticsView →
- Whether either bus comes soonEasyProbabilityRandom VariablesView →
- Which side holds the heavy weightEasyProbabilityCombinatoricsView →
- Winning by a growing marginEasyProbabilityBrainteasersView →
- A CLT tail probabilityMediumStatisticsView →
- A convexity gap by JensenMediumRandom VariablesExpected ValueView →
- A cube root by tangent lineMediumCalculusView →
- A ladder slipping in oilMediumCalculusView →
- A large power, modular orderMediumProgramming & DSAView →
- An integral by symmetryMediumCalculusView →
- Backing out a margin-free probabilityMediumMarket Making & Betting GamesView →
- Balancing six- and eight-sided diceMediumExpected ValueBrainteasersView →
- Balloon related ratesMediumCalculusView →
- Buyer count in a thinned arrival streamMediumProbabilityStochastic ProcessesView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Cash-and-carry arbitrageMediumFinance & DerivativesView →
- Cats and dogs on the streetMediumBrainteasersView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Correlation of overlapping sumsMediumRandom VariablesStatisticsView →
- Cutting a cube into 27MediumBrainteasersView →
- Dice payoff via WaldMediumExpected ValueStochastic ProcessesView →
- Digits multiplying to half the numberMediumBrainteasersView →
- Distinct birthdays representedMediumProbabilityExpected ValueView →
- Distinct faces in five rollsMediumCombinatoricsExpected ValueView →
- Distributing candies with a capMediumCombinatoricsView →
- Eight dice summing to twelveMediumProbabilityCombinatoricsView →
- Empty boxesMediumExpected ValueView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Expected exponential of Brownian motionMediumStochastic ProcessesView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- Expected maximum of three diceMediumRandom VariablesExpected ValueView →
- Expected maximum of two diceMediumRandom VariablesExpected ValueView →
- Expected median of three diceMediumProbabilityExpected ValueView →
- Expected value of the highest cardMediumProbabilityExpected ValueView →
- First consecutive repeatMediumProbabilityExpected ValueView →
- First head on an even flipMediumProbabilityView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- Forward price with a cash dividendMediumFinance & DerivativesView →
- HT before HH in coin flipsMediumProbabilityStochastic ProcessesView →
- How many stack outputs?MediumProgramming & DSAView →
- Implicit differentiation on a circleMediumCalculusView →
- Largest pen against a riverMediumCalculusView →
- Limit of x ln x as x to 0+MediumCalculusView →
- MLE at a boundaryMediumStatisticsCalculusView →
- Monotone paths across a gridMediumCombinatoricsView →
- Neither die exceeds fourMediumProbabilityRandom VariablesView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- Paid only if the last roll winsMediumExpected ValueView →
- Pair at a round tableMediumCombinatoricsView →
- Poisson thinning: exactly two large ordersMediumRandom VariablesView →
- Rare-event Poisson approximationMediumProbabilityRandom VariablesView →
- Rate of a growing shadowMediumCalculusView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Right angles in 12 hoursMediumBrainteasersView →
- Rolling a 5-sided die to reach fiveMediumProbabilityExpected ValueView →
- Rolling until two rolls differ by twoMediumProbabilityExpected ValueView →
- Sharpe ratio in a marble gameMediumExpected ValueStatisticsView →
- Sum of 10 with three diceMediumProbabilityCombinatoricsView →
- The gold chainMediumBrainteasersView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- Three dots, exactly one shared edgeMediumProbabilityCombinatoricsView →
- Two ropes, 45 minutesMediumBrainteasersView →
- Two trains and a flyMediumBrainteasersView →
- Two uniforms summing past 1.5MediumProbabilityCalculusView →
- Variance of a coin-gated payoffMediumRandom VariablesStatisticsView →
- Variance of an aggregate Poisson totalMediumRandom VariablesStochastic ProcessesView →
- Volatility smile meaningMediumStatisticsFinance & DerivativesView →
- Which desk books the larger dayMediumRandom VariablesStatisticsView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A flea's shortest escape across a boxHardBrainteasersCalculusView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A triangle of consecutive integersHardBrainteasersView →
- Cats and miceHardBrainteasersView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Measuring two pintsHardBrainteasersView →
- Rolling until two rolls are closeHardProbabilityExpected ValueView →
- Shortest of three piecesHardProbabilityRandom VariablesView →
- Six pieces, none past a halfHardProbabilityRandom VariablesView →
- The reroll advantage in a die duelHardProbabilityMarket Making & Betting GamesView →
- Weighings for the odd beanHardBrainteasersView →
- Will the three-legged table stand?HardProbabilityView →
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