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, 156 of them free to practise right now. 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 in a rowEasyProbabilityExpected 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 →
- Balancing six- and eight-sided diceMediumExpected ValueBrainteasersView →
- Bridge and torchMediumBrainteasersView →
- Capturing the spreadMediumMarket Making & Betting GamesView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Cats and dogs on the streetMediumBrainteasersView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Cutting a cube into 27MediumBrainteasersView →
- 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 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 →
- Gamma-scalping a round tripMediumFinance & DerivativesView →
- Implied vol from a straddle quoteMediumFinance & DerivativesView →
- Locking a profit by hedging after the odds moveMediumExpected ValueMarket Making & Betting GamesView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- Pay to play with a capMediumExpected ValueMarket Making & Betting GamesView →
- Pricing the higher of two diceMediumExpected ValueMarket Making & Betting GamesView →
- Profit on a bull call spreadMediumFinance & DerivativesView →
- Profit on a risk reversalMediumFinance & DerivativesView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- 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 multiples of 3 or 5MediumBrainteasersView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- Three dots on a squareMediumProbabilityCombinatoricsView →
- Three rolls, keep the lastMediumExpected ValueView →
- Three-jug measuringMediumBrainteasersView →
- Two ropes, 45 minutesMediumBrainteasersView →
- Variance of a coin-gated payoffMediumRandom 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 →
- A convexity gap by JensenMediumRandom VariablesExpected Value Premium
- A cube root by tangent lineMediumCalculus Premium
- Ants on a stickMediumBrainteasers Premium
- Backing out a margin-free probabilityMediumMarket Making & Betting Games Premium
- Balloon related ratesMediumCalculus Premium
- Break-even half-spread from toxic flowMediumProbabilityExpected Value Premium
- Break-even half-spread under adverse selectionMediumExpected ValueMarket Making & Betting Games Premium
- Buyer count in a thinned arrival streamMediumProbabilityStochastic Processes Premium
- Calendar spread intuitionMediumFinance & Derivatives Premium
- Cash-and-carry arbitrageMediumFinance & Derivatives Premium
- Cash-and-carry arbitrage profitMediumFinance & Derivatives Premium
- Correlation of overlapping sumsMediumRandom VariablesStatistics Premium
- Delta-hedge a two-leg option bookMediumFinance & Derivatives Premium
- Expected maximum of three diceMediumRandom VariablesExpected Value Premium
- Expected revenue of a Vickrey auctionMediumProbabilityExpected Value Premium
- Fair price of a die with one re-rollMediumExpected ValueMarket Making & Betting Games Premium
- Fair value after two informed buysMediumMarket Making & Betting Games Premium
- Four distinct birth monthsMediumProbabilityCombinatorics Premium
- Frog in the wellMediumBrainteasers Premium
- HT before HH in coin flipsMediumProbabilityStochastic Processes Premium
- Inventory skewMediumMarket Making & Betting Games Premium
- Limit of x ln x as x to 0+MediumCalculus Premium
- MLE at a boundaryMediumStatisticsCalculus Premium
- Neither die exceeds fourMediumProbabilityRandom Variables Premium
- Optimal quote widthMediumMarket Making & Betting Games Premium
- Pair at a round tableMediumCombinatorics Premium
- Prime sumMediumProbability Premium
- Rare-event Poisson approximationMediumProbabilityRandom Variables Premium
- Right angles in 12 hoursMediumBrainteasers Premium
- Sum of 10 with three diceMediumProbabilityCombinatorics Premium
- The gold chainMediumBrainteasers Premium
- The missing dollarMediumBrainteasers Premium
- Two trains and a flyMediumBrainteasers Premium
- Two uniforms summing past 1.5MediumProbabilityCalculus Premium
- Volatility smile meaningMediumStatisticsFinance & Derivatives Premium
- Which desk books the larger dayMediumRandom VariablesStatistics Premium
Widen the search
This set is a slice of two larger ones. If it is too narrow, start here instead:
Practise these free
Create a free account to check your answers, track what you have solved, and run the timed simulators. Premium unlocks a full worked solution for every question.