Numerical Reasoning Tests Interview Questions for Traders
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 traders.
192 questions, all free to practise. The split is 104 easy, 77 medium, 11 hard. The topics that come up most are probability (90), expected value (48), brainteasers (36), combinatorics (29).
- 1 immediately before 2EasyProbabilityCombinatoricsView →
- A compound-interest limit in disguiseEasyCalculusView →
- A die decides how many balls to drawEasyProbabilityExpected ValueView →
- 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 one-sided percentile cutoffEasyRandom VariablesStatisticsView →
- A point is established in crapsEasyProbabilityView →
- A sum of four before a sum of twoEasyProbabilityView →
- A tail of a sum of normalsEasyRandom VariablesStatisticsView →
- A three given a sum divisible by threeEasyProbabilityConditional Probability & ExpectationView →
- Adjacent faces on two diceEasyProbabilityView →
- An even sum given a five appearsEasyProbabilityConditional Probability & ExpectationView →
- Ants on a squareEasyProbabilityBrainteasersView →
- At least one 3 and at least one 5EasyProbabilityView →
- At least one blue and one greenEasyProbabilityCombinatoricsView →
- At least two in the windowEasyProbabilityStochastic ProcessesView →
- Average speed over three lapsEasyBrainteasersView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Break-even uninformed fraction against pick-offsEasyMarket Making & Betting GamesView →
- Bull spread net profitEasyFinance & DerivativesView →
- Butterfly spread maximum profitEasyFinance & DerivativesView →
- Clock angle at 3:15EasyBrainteasersView →
- Coin count past two sigmaEasyRandom VariablesStatisticsView →
- Coin rolling around a coinEasyBrainteasersView →
- Committee with both sexesEasyCombinatoricsView →
- Comparing implied vols from two quotesEasyFinance & DerivativesView →
- Conditioning a uniform waitEasyProbabilityRandom VariablesView →
- Counting arithmetic triplesEasyProbabilityCombinatoricsView →
- Dots on distinct edgesEasyProbabilityCombinatoricsView →
- Even first die given a sum of eightEasyConditional Probability & ExpectationExpected ValueView →
- Even sum bigger than sevenEasyProbabilityView →
- Exactly one head given at least oneEasyProbabilityConditional Probability & ExpectationView →
- 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 →
- Expected profit on a scratch ticketEasyExpected ValueMarket Making & Betting GamesView →
- Expected sum given a sixEasyProbabilityExpected ValueView →
- Face card or heartEasyProbabilityView →
- Fair mid on a dice product that voids on doublesEasyProbabilityExpected ValueView →
- Fair price of a dice-product gameEasyExpected ValueMarket Making & Betting GamesView →
- Fair price of a heads-majority betEasyProbabilityExpected ValueView →
- Fair price of a high-faces-only dice sumEasyExpected ValueMarket Making & Betting GamesView →
- Fair price of a sum-divisible-by-three betEasyExpected ValueMarket Making & Betting GamesView →
- Finding the light coinEasyBrainteasersView →
- Four dice summing to twentyEasyProbabilityCombinatoricsView →
- Gap between two dice, given they differEasyConditional Probability & ExpectationExpected ValueView →
- Guessing a number with high-low hintsEasyBrainteasersProgramming & DSAView →
- Hands directly oppositeEasyBrainteasersView →
- Handshakes across two groupsEasyCombinatoricsView →
- How many rolls to make the 6-bet favorableEasyProbabilityMarket Making & Betting GamesView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Keep the d8 or gamble on the d12?EasyProbabilityExpected ValueView →
- Landing in the ringEasyProbabilityView →
- Lapping on the trackEasyBrainteasersView →
- Matching locks to keysEasyBrainteasersView →
- Merging two round-robinsEasyCombinatoricsView →
- Normalizing a tilted densityEasyRandom VariablesCalculusView →
- One blue die matches the redEasyProbabilityView →
- One re-roll allowedEasyExpected ValueView →
- Origin between two pointsEasyProbabilityView →
- Paid the last roll before you stopEasyProbabilityExpected ValueView →
- Pairs who swap hatsEasyRandom VariablesExpected ValueView →
- Product divisible by fourEasyProbabilityView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Rolling a die to size the next dieEasyConditional Probability & ExpectationExpected ValueView →
- Rolling until a high face, at a costEasyProbabilityExpected ValueView →
- Rolling until you match the first rollEasyProbabilityExpected ValueView →
- Rolls until an even sumEasyProbabilityExpected ValueView →
- Rope lifted off the EarthEasyBrainteasersView →
- Same side four timesEasyProbabilityView →
- Seating with a gapEasyCombinatoricsView →
- Second roll beats the firstEasyProbabilityView →
- Sizing a put–call parity mispricingEasyFinance & DerivativesView →
- Smallest multiple of 77 past 700000EasyBrainteasersView →
- Socks for a matching trioEasyCombinatoricsBrainteasersView →
- Spread of a coin-flip payoffEasyRandom VariablesStatisticsView →
- Squared payout on even facesEasyRandom VariablesExpected ValueView →
- Stop at the first girlEasyProbabilityView →
- Streak then a head countEasyProbabilityConditional Probability & ExpectationView →
- Tangent-minus-sine third-order limitEasyCalculusView →
- The clock that runs fastEasyBrainteasersView →
- The higher die shows a fourEasyProbabilityView →
- The second draw is redEasyProbabilityConditional Probability & ExpectationView →
- The weight of the fishEasyBrainteasersView →
- Three dice, increasingEasyProbabilityCombinatoricsView →
- Three primes in six rollsEasyProbabilityView →
- Timing the revolverEasyBrainteasersView →
- Top three dice summing to eighteenEasyProbabilityCombinatoricsView →
- Triangles across two linesEasyCombinatoricsView →
- Two mismatched diceEasyProbabilityView →
- Unchanged after ten swingsEasyProbabilityBrainteasersView →
- Variance of a reciprocal uniformEasyRandom VariablesStatisticsView →
- Variance of a union indicatorEasyRandom VariablesStatisticsView →
- Variance of a weighted dice combinationEasyRandom VariablesStatisticsView →
- 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 →
- Who wins the first head?EasyProbabilityView →
- Winning by a growing marginEasyProbabilityBrainteasersView →
- A 5 before a 7MediumProbabilityView →
- A convexity gap by JensenMediumRandom VariablesExpected ValueView →
- A cube root by tangent lineMediumCalculusView →
- Ants on a stickMediumBrainteasersView →
- Backing out a margin-free probabilityMediumMarket Making & Betting GamesView →
- Balancing six- and eight-sided diceMediumExpected ValueBrainteasersView →
- Balloon related ratesMediumCalculusView →
- Break-even half-spread from toxic flowMediumProbabilityExpected ValueView →
- Break-even half-spread under adverse selectionMediumExpected ValueMarket Making & Betting GamesView →
- Bridge and torchMediumBrainteasersView →
- Buyer count in a thinned arrival streamMediumProbabilityStochastic ProcessesView →
- Calendar spread intuitionMediumFinance & DerivativesView →
- Capturing the spreadMediumMarket Making & Betting GamesView →
- 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 →
- Delta-hedge a two-leg option bookMediumFinance & DerivativesView →
- Dice payoff via WaldMediumExpected ValueStochastic ProcessesView →
- Distributing candies with a capMediumCombinatoricsView →
- Eight dice summing to twelveMediumProbabilityCombinatoricsView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- 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 revenue of a Vickrey auctionMediumProbabilityExpected ValueView →
- Expected value of the highest cardMediumProbabilityExpected ValueView →
- Fair price of a payout that doubles per headMediumExpected ValueMarket Making & Betting GamesView →
- Fair value after two informed buysMediumMarket Making & Betting GamesView →
- First consecutive repeatMediumProbabilityExpected ValueView →
- First head on an even flipMediumProbabilityView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- Forward price with a cash dividendMediumFinance & DerivativesView →
- Four distinct birth monthsMediumProbabilityCombinatoricsView →
- Frog in the wellMediumBrainteasersView →
- Gamma-scalping a round tripMediumFinance & DerivativesView →
- HT before HH in coin flipsMediumProbabilityStochastic ProcessesView →
- Implied vol from a straddle quoteMediumFinance & DerivativesView →
- Inventory skewMediumMarket Making & Betting GamesView →
- Limit of x ln x as x to 0+MediumCalculusView →
- Locking a profit by hedging after the odds moveMediumExpected ValueMarket Making & Betting GamesView →
- MLE at a boundaryMediumStatisticsCalculusView →
- Neither die exceeds fourMediumProbabilityRandom VariablesView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- Optimal quote widthMediumMarket Making & Betting GamesView →
- Paid only if the last roll winsMediumExpected ValueView →
- Pair at a round tableMediumCombinatoricsView →
- Pay to play with a capMediumExpected ValueMarket Making & Betting GamesView →
- Prime sumMediumProbabilityView →
- Product of two dice, doubled on doublesMediumExpected ValueMarket Making & Betting GamesView →
- Profit on a bull call spreadMediumFinance & DerivativesView →
- Profit on a risk reversalMediumFinance & DerivativesView →
- Rare-event Poisson approximationMediumProbabilityRandom VariablesView →
- 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 →
- Sum of multiples of 3 or 5MediumBrainteasersView →
- The gold chainMediumBrainteasersView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The missing dollarMediumBrainteasersView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- Three dots, exactly one shared edgeMediumProbabilityCombinatoricsView →
- Three-jug measuringMediumBrainteasersView →
- Two ropes, 45 minutesMediumBrainteasersView →
- Two trains and a flyMediumBrainteasersView →
- Two uniforms summing past 1.5MediumProbabilityCalculusView →
- Variance of a coin-gated payoffMediumRandom VariablesStatisticsView →
- Volatility smile meaningMediumStatisticsFinance & DerivativesView →
- Which desk books the larger dayMediumRandom VariablesStatisticsView →
- Winner's curseMediumMarket Making & Betting GamesView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A triangle of consecutive integersHardBrainteasersView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- 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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