What's 17 × 19?
Core323. Use (18−1)(18+1)+? No, simplest: 17×19 = 17×20 − 17 = 340 − 17 = 323. Practise fast decomposition (round to a friendly number, adjust). Speed with accuracy under pressure is the point.
Sales & Trading
Markets desks. Fast mental maths, probability, market awareness and how you react under pressure and to being wrong.
A sample of the Sales & Trading bank: the first 3 questions of every topic, with the model answers. 304 questions in total.
Mental maths
42 questions in this topic
What's 23 × 27?
Intermediate621. Use the difference-of-squares trick: 23 × 27 = (25 − 2)(25 + 2) = 625 − 4 = 621. Spotting that both numbers straddle a round 25 turns a hard multiply into a trivial one, exactly the pattern recognition desks want.
What's 26 × 24?
Intermediate624. Difference of squares: (25−1)(25+1) = 625 − 1 = 624. Spot numbers straddling a round midpoint to turn a hard multiply into a subtraction.
39 more questions on Mental maths, with model answers, inside.
Probability
65 questions in this topic
A fair coin is flipped until the first head. What's the expected number of flips?
Intermediate2. For a geometric distribution with p = 0.5, expected flips = 1/p = 2. Be ready to derive E = 1 + (1−p)E as well.
You roll two dice. What's the probability the sum is 7?
Core6/36 = 1/6. Seven is the most likely sum, six combinations out of 36. Know the distribution of two-dice sums.
I'll pay you the value of a single die roll. What would you pay to play?
IntermediateExpected value = (1+2+3+4+5+6)/6 = 3.5, so a risk-neutral price is 3.5. In a market-making game you'd quote a spread around it (e.g., bid 3, offer 4) and adjust as they trade against you.
62 more questions on Probability, with model answers, inside.
Markets
70 questions in this topic
Where is the S&P / a key rate, and what's moving markets?
CoreKnow roughly where major indices, key central-bank rates and major FX/commodities sit, and the one or two themes driving them right now. You don't need precision to the decimal, you need to clearly follow markets and reason about drivers.
Make me a market on the number of countries in the EU (quote a two-way).
IntermediateQuote a tight two-way you'd be happy to trade both sides of, e.g. "26 at 28" (bid 26, offer 28), around your best estimate (27). If they lift your offer, you're now short and should shade higher; if they hit your bid, shade lower. The game tests calibration, spread discipline and how you update, not trivia.
Why do bond prices fall when yields rise?
IntermediateA bond pays fixed coupons; if market yields rise, new bonds pay more, so the existing bond's fixed stream is worth less, its price falls until its yield matches the market. Price and yield are two ways of quoting the same thing and move inversely. Longer-duration bonds move more for a given yield change.
67 more questions on Markets, with model answers, inside.
Fit
36 questions in this topic
Why sales & trading, and sales or trading?
CoreTrading: fast decisions, risk-taking, being right/wrong in real time, quantitative. Sales: relationships, market intuition, connecting clients to ideas/flow. Pick honestly and back it with your strengths and how you handle pressure and being wrong.
How do you handle losing money on a trade?
IntermediateSeparate process from outcome: was the trade wrong, or right but unlucky? Cut when the thesis breaks or the stop is hit, don't average into a loser to feel right, and size so no single trade can hurt you. Desks want composure and discipline under P&L pressure, not bravado. A concrete example of staying rational after a loss lands well.
How do you react to being wrong and losing money?
IntermediateSeparate process from outcome, cut when the thesis or stop is hit rather than averaging into a loser to feel right, and size so no single trade can hurt you. Give a concrete example of staying disciplined after a loss. Desks want composure and risk discipline under P&L pressure, not bravado or paralysis.
33 more questions on Fit, with model answers, inside.
Market-making
21 questions in this topic
Make me a market on the number of windows in this building.
IntermediateQuote a two-way you'd trade both sides of, e.g. "180 at 220" around your estimate. If they lift your offer, you're short and shade up; if they hit your bid, shade down. The game tests calibration, spread discipline (tight enough to be real, wide enough for uncertainty) and how you update on their flow: not the true number.
I roll two dice and pay you the product. What's your market?
HardE[product] = E[die]² = 3.5² = 12.25 (the dice are independent). Quote a spread around ~12.25, say "11 at 13.5", and skew as they trade. Don't forget independence lets you square the mean; the variance is high, so keep the spread respectably wide.
Why do you widen your spread when someone keeps trading against you?
AdvancedPersistent one-way flow signals they may know something you don't (adverse selection), so you widen and shade your quote in their direction to protect against being repeatedly picked off. Tight spreads win volume but lose to informed flow: managing that trade-off is the core skill of making markets.
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Brainteasers
19 questions in this topic
100 people in a circle, every second person is eliminated. Where do you stand to survive?
ExpertThe Josephus problem. For n = 100, the safe position is 2×(100 − 2^6) + 1 = 2×36 + 1 = 73 (largest power of two ≤ 100 is 64). They want you to spot the power-of-two structure and reason it, not memorise: walk through small cases to derive it.
You have 8 balls, one heavier. Find it in 2 weighings on a balance.
HardSplit into 3-3-2. Weigh 3 vs 3: if balanced, the heavy one is in the 2: weigh them (1 weighing). If one side is heavier, take those 3, weigh 1 vs 1: heavier side or the odd one out. Two weighings suffice. The trick is thirds, not halves, because each weighing has three outcomes.
A rope burns unevenly in exactly 60 minutes. How do you measure 45 minutes with two ropes?
HardLight rope A at both ends and rope B at one end simultaneously. A burns out in 30 min; at that instant light B's other end: B's remaining half now burns from both ends in 15 min. 30 + 15 = 45. The insight: burning both ends halves the time regardless of unevenness.
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Trading
22 questions in this topic
What's the difference between a limit order and a market order?
IntermediateA market order executes immediately at the best available price (certainty of execution, uncertain price); a limit order executes only at your specified price or better (certain price, uncertain execution). Market orders pay the spread and can suffer slippage in thin markets; limit orders may never fill. Choose based on urgency vs price sensitivity.
What is bid-ask spread and what makes it wide or narrow?
IntermediateThe gap between the best buy (bid) and sell (ask) prices: the market-maker's compensation and a cost to the taker. It narrows with high liquidity, volume and competition, and widens with volatility, illiquidity, uncertainty and adverse-selection risk. Spread is the price of immediacy.
You're long a position and bad news hits. Walk me through your thinking.
AdvancedRe-assess fast: is the news thesis-breaking or noise/overreaction? Check your stop and risk limits, the position's size relative to the book, and liquidity to exit. Decide to cut, hold, or add on conviction, but don't freeze or average down to feel right. Process over emotion: manage the risk first, then judge whether the opportunity improved or the thesis broke.
19 more questions on Trading, with model answers, inside.
Estimation
12 questions in this topic
How many tennis balls fit in a typical car?
IntermediateEstimate the car's interior usable volume (~2-3 m³), a tennis ball's volume (~0.00015 m³, from ~6.5cm diameter), divide, and apply ~65% packing efficiency → roughly 10,000-13,000. State assumptions, do the arithmetic aloud, sanity-check the magnitude. Structure and packing-factor awareness are the point.
Estimate the number of practicing dentists in the United States.
HardThe US population is about 330 million, if there's roughly one dentist for every 1,500 to 2,000 people, a ratio consistent with regular checkup demand, that implies somewhere around 165,000 to 220,000 dentists. Build the ratio from a plausible visit frequency, most people see a dentist roughly once or twice a year, and a dentist's daily patient capacity, rather than guessing the total directly.
Estimate the number of yellow taxis operating in New York City.
IntermediateNYC's medallion system historically capped yellow cabs at around 13,000, a figure worth just knowing roughly if you can, but if reasoning from scratch, estimate from city population and typical taxi usage rates in a dense urban core, landing in a similar five-figure range. This is a case where recalling an approximate real anchor beats a pure Fermi build-up if you have it.
9 more questions on Estimation, with model answers, inside.
Market structure
17 questions in this topic
What's the difference between a market-maker and a broker?
IntermediateA market-maker quotes two-way prices and takes the other side of trades from its own book (principal), earning the spread and bearing inventory risk. A broker acts as agent, matching buyers and sellers for a commission without taking principal risk. Market-makers provide liquidity and immediacy; brokers provide access and execution. Many firms do both, separated by function.
What is slippage and how do you minimise it?
AdvancedSlippage is the gap between the expected and actual execution price, caused by market impact and moves during execution: worse for large orders in illiquid names. Minimise it by working the order over time (VWAP/TWAP algos), using limit orders, trading in liquid windows, and splitting size. Execution quality is a real cost, especially for large or urgent trades.
Why might a large order move the market against you, and how do you hide it?
AdvancedA large buy consumes available offers and signals demand, pushing the price up before you're filled (market impact and information leakage). You reduce it by slicing the order over time, using dark pools/algos to avoid showing size, and trading patiently in liquid periods. Concealing intent and minimising footprint is core execution skill.
14 more questions on Market structure, with model answers, inside.
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