Venture Capital puzzles, solved step by step
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042A mental maths set from a first-round interview: work out 49 x 51, 998 x 1,002 and 12.5% of Rs 3,680 crore, each inside ten seconds.General AtlanticNew York · 2026
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What is 998 x 1,002?
Show the worked solution
2,499, then 9,99,996, then Rs 460 crore. The first two use the same shortcut: numbers equally spaced either side of a round number multiply to its square minus the gap squared, so 49 x 51 is 2,500 minus 1, and 998 x 1,002 is 10,00,000 minus 4. The third is a fraction in disguise: 12.5% is one eighth, so halve Rs 3,680 crore three times, to 1,840, 920 and 460.
Why does 49 x 51 come out one short of 2,500?
Picture a square garden 50 metres a side. Take a one-metre strip off the bottom, 50 square metres, and lay it along the right-hand side. It only fits for 49 metres, so one square metre is left over. A rectangle 49 by 51 is a 50 by 50 square with one corner square missing, so the product is 2,500 minus 1, or 2,499. The same picture works for any pair spread evenly around a round number: the product is the middle number squared minus the gap squared.
The relationshipa the round number in the middle, 50 or 1,000 b how far each factor sits from it, 1 or 2 a squared minus b squared the product, always slightly below the square What it says in wordsTwo numbers spread evenly either side of a round number multiply to that number squared, less the gap squared.49 x 51 is a 50 by 50 square with one unit square missing, so it equals 2,499, and 12.5% of Rs 3,680 crore is one of eight equal blocks, Rs 460 crore, found by halving three times. How do you take 12.5% of anything in a few seconds?
Recognise the fraction first. 12.5% is one eighth, and dividing by eight is the same as halving three times, which is easier to do aloud than any long division. Rs 3,680 crore halves to 1,840, then 920, then 460. Keep a short list of these anchors ready: 12.5% is an eighth, 37.5% three eighths, 16.7% a sixth, 6.25% a sixteenth. Interviewers who give percentage questions usually pick one of them, because the speed of recognising the fraction is what they are testing.
What is the interviewer actually checking?
Speed sets are less about arithmetic than about whether you look for structure before you calculate. Saying the shortcut out loud, square minus one, or halve three times, shows a method that will also work on the next question. Two habits help. Check the size of your answer against an anchor: 49 x 51 must sit just under 2,500. And say the number back with its units, Rs 460 crore, not just 460. The limit of these tricks is that they only work on numbers chosen to suit them; for awkward numbers, round and say so.
Where candidates lose it
The common loss on the products is grinding through long multiplication and running out of time, or writing 10,00,004 because the sign of the correction is guessed. The product of numbers either side of a round number is always below its square.
On the percentage, candidates multiply 3,680 by 0.125 digit by digit and fumble. Name the fraction, one eighth, and halve three times; the clock is part of the question.
What the interviewer asks next
- Work out 97 x 103 and 4.95 x 5.05 the same way.
- What is 37.5% of Rs 2,400 crore?
- Estimate 1,999 squared in your head.
Asked at General Atlantic, Generalist, New York, 2026 (Wall Street Oasis):
The first round was behavioral with mental math at the end.
065An online aptitude test has 50 questions in 12 minutes, five options each, and no penalty for wrong answers. You can answer about 30 questions carefully in the time, at 85% accuracy. Should you guess the other 20, and what is your expected score?Vista Equity PartnersAustin · 2022
Try it first
What is your expected score if you guess the last 20?
Show the worked solution
Yes, guess every remaining question; the expected score rises from 25.5 to 29.5. Your 30 careful answers at 85% are worth 25.5 points. A blind guess on a five-option question is right one time in five, and a wrong answer costs nothing, so 20 guesses add 20 x 0.2, or 4 expected points. A blank is a sure zero. The only real decision is leaving yourself the last 30 seconds to fill them in.
Why is a blind guess worth anything at all?
A free raffle ticket is worth taking even if the odds are poor, because it costs nothing. When wrong answers carry no penalty, every guess has a positive expected value, one point times the chance of being right, and a blank has an expected value of exactly zero. With five options that chance is 1 in 5, so each guess is worth 0.2 points and twenty are worth 4. On a 50-question test, 4 points is often the gap between two scoring bands.
Thirty careful answers at 85% give 25.5 expected points, and filling the remaining 20 with blind guesses adds 20 x 0.2 = 4 more, lifting the expected score to 29.5 at no cost because wrong answers are not penalised. The relationship30 x 0.85 careful answers times your accuracy 20 x 1/5 blind guesses times the chance a random pick is right What it says in wordsAdd what the careful answers are worth to what the guesses are worth; blanks add nothing.What changes if wrong answers are penalised, and how do you manage the clock?
Suppose a wrong answer cost a quarter of a point. A blind guess would then be worth 0.2 minus 0.8 x 0.25, which is exactly zero. The rule is to guess whenever the chance of being right times the reward beats the chance of being wrong times the penalty, and eliminating even one option tips a penalised guess back into positive value. On the clock: 12 minutes for 50 questions is 14.4 seconds each. Skip any question that will take more than about 30 seconds, come back if time allows, and stop answering carefully with half a minute left to fill every blank.
Two honest notes. The 4 points are an average: 20 guesses have a standard deviation of about 1.8 points, and there is roughly a 1% chance none of them land. And the no-penalty rule is the premise of this question; tests differ, so check the instructions of the one you are sitting before deciding.
Where candidates lose it
The trap is leaving blanks out of a sense that guessing is unserious. On a no-penalty test that throws away free expected points, and the people who score well on these tests always fill every answer.
The second loss is spending too long on hard questions early. At 14.4 seconds a question, one stubborn item can cost you three easy ones; skip, mark and return.
What the interviewer asks next
- If a wrong answer cost a quarter point, would you still guess?
- You can eliminate one option on each of the 20. What is the guess value now?
- Would you rather answer 35 at 75% accuracy or 30 at 85%?
Asked at Vista Equity Partners, Technology, Media and Telecom, Austin, 2022 (Wall Street Oasis):
Application requires a CCAT, 50 questions in 12 minutes.
096A timed cognitive test item: if 4 associates screen 60 pitch decks in 3 hours, how many decks do 6 associates screen in 5 hours, working at the same rate?Seed and early-stage VCMulti-stage VC
Try it first
Answer in under thirty seconds.
Show the worked solution
150 decks. Reduce everything to one unit first: 4 associates working 3 hours is 12 associate-hours, and 60 decks over 12 is 5 decks per associate-hour. Six associates for five hours is 30 associate-hours, so 30 x 5 = 150. As a check, scale the original: 60 x 6/4 x 5/3 is also 150. This assumes everyone works at the same steady rate.
Why reduce to a rate per associate-hour?
If 2 cooks make 40 rotis in an hour, one cook makes 20 an hour, and any kitchen size or shift length follows from that one number. Work problems become simple once you find the output of one worker in one unit of time, because the total is then that rate times workers times hours. Here 60 decks came from 4 x 3 = 12 associate-hours, so the rate is 5 decks per associate-hour. Everything else is multiplication.
Four associates working three hours make 12 associate-hours, and 60 decks over 12 cells is 5 decks per associate-hour; six associates working five hours make 30 such cells, so they screen 30 x 5 = 150 decks. The relationshipD decks screened r decks per associate-hour a number of associates h hours worked What it says in wordsOutput is the rate of one person for one hour, times the people, times the hours.How do you avoid the slip under time pressure?
Ask which way each change pushes the answer before you multiply. More associates and more hours both raise output, so both ratios must be greater than one: 6/4 and 5/3, never 4/6 or 3/5. The fast wrong answer, 90, applies the 6/4 and stops. On a timed test the danger is not hard arithmetic but a missed step, so a five-second check that the answer moved in the right direction by roughly the right amount is worth it: one and a half times the people for two thirds more time should give about two and a half times the output, and 60 x 2.5 is 150.
Where would this break down in a real deal team?
The model assumes every associate screens at the same steady pace and that output scales with hours. Real screening slows late in a long day, and a bigger team spends time coordinating and avoiding duplicate work. Saying so is unnecessary on the test itself, but it is the right instinct if the same question comes up in an interview: the arithmetic answer is the ceiling, and the real number is usually lower.
Where candidates lose it
The common slip is to scale for only one of the two changes, giving 90 from the associates alone or 100 from the hours alone. Under a clock, candidates grab the first ratio they see and move on.
The other loss is inverting a ratio, as if more associates meant fewer decks. Find the unit rate first and the direction takes care of itself.
What the interviewer asks next
- How many associates are needed to screen 300 decks in 4 hours?
- If two of the six associates work at half speed, how many decks are screened in 5 hours?
- A partner reviews 20% of screened decks at 3 decks an hour. How many partner-hours does the 5-hour session create?
