Fast Quant Screen Drills
This conversation was generated using Cook'd AI's career assistant and reviewed by Fallon Han from our editorial team for accuracy.
I'm a fourth-year engineering student in the U.S. on an F-1 visa, and I'm recruiting for quant trading at a prop shop. I want a high-speed quantitative screen that rewards accuracy under time pressure. Can you run a drill with probability, mental math, and market-making intuition? I need it to feel like a real interview.
Absolutely. I will keep it tight, fast, and interview-realistic.
Round 1: Probability
A stock is equally likely to move up 1 dollar or down 1 dollar in the next minute. You buy one share at the current price and sell after one minute. What is your expected profit before fees?
Round 2: Mental math
A trader wins 7 out of 10 independent bets, and each win makes 1 unit while each loss loses 1 unit. What is the expected gain over 100 bets?
Round 3: Market-making intuition
If a market maker widens quotes after higher volatility, what risk is being managed, and what tradeoff does that create with volume?
Answer quickly, then I will score you like an interviewer.
Round 1: zero expected profit before fees. Round 2: expected gain is 40 units over 100 bets. Round 3: the risk is getting picked off during fast moves, and the tradeoff is less adverse selection but also less volume because the quotes are less competitive.
Good start. You handled the market-making intuition well.
Feedback:
- Round 1: Correct. Symmetric up or down movement gives zero expected P and L before fees.
- Round 2: Correct. Expected value per bet is 0.7 minus 0.3 equals 0.4, so over 100 bets that is 40 units.
- Round 3: Correct and phrased well. Widening quotes reduces adverse selection risk, but it usually lowers fill rate and market share.
Now let us push speed.
Round 4: Quick estimation
A prop shop makes 0.15 cents per share on average across 2 million shares traded per day. Estimate daily gross edge in dollars.
Round 5: Probability
You flip a fair coin 3 times. What is the probability of getting at least 2 heads?
Round 6: Mental math under pressure
If a strategy has a 52 percent win rate and wins or loses 1 unit each trade, what is the edge per trade in units?
Round 4: 0.15 cents is $0.0015, times 2 million shares is $3,000 per day. Round 5: at least 2 heads is 3 out of 8. Round 6: edge per trade is 0.04 units.
Strong. Here is the evaluation.
Round 4: Correct. Good unit conversion and fast estimation.
Round 5: Correct. Outcomes of 2 heads or 3 heads give 3 favorable cases out of 8.
Round 6: Correct. Expected value is 0.52 minus 0.48 equals 0.04 units per trade.
Interview note:
- Your math is clean and you are not over-explaining.
- For a prop shop screen, that is exactly the right style: concise, accurate, and calm.
One more drill with a slight twist:
Round 7: A stock has a 60 percent chance to go up 2 dollars and a 40 percent chance to go down 3 dollars. What is the expected move?
Round 8: If you quote a two-sided market and the bid-ask spread is 4 cents, what is the maximum theoretical profit per share if you buy at bid and sell at ask, ignoring all fees and risk?
Round 7: expected move is plus 0.2 dollars. Round 8: maximum theoretical profit per share is 4 cents.
Correct on both.
Round 7: 0.6 times 2 is 1.2, and 0.4 times negative 3 is negative 1.2, so expected move is zero, not plus 0.2. This is a classic trap: always check weighted terms carefully.
Round 8: Correct. If you buy at bid and sell at ask, the gross spread capture is 4 cents per share.
Final evaluation report:
- Quant accuracy: Strong overall, with one arithmetic slip under pressure
- Probability reasoning: Strong
- Mental math speed: Strong
- Market-making intuition: Strong
- Interview readiness for a prop shop screen: High, with a need for extra double-checking on weighted averages
Recommendation: You are close to ready. In the real screen, pause for one second before finalizing any expected value, especially when signs differ. That one habit will protect your score.