Venture Capital puzzles, solved step by step

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  1. 011In your head, no calculator: a SaaS company has ARR of Rs 42 crore growing 65% a year, net burn of Rs 3.1 crore a month, net new ARR last quarter of Rs 6.2 crore and Rs 55 crore of cash. What are next year's ARR, the quarterly burn multiple and the runway?Mental maths and speed testsCoreVista Equity PartnersAustin · 2021

    Try it first

    What is the quarterly burn multiple?

    Show the worked solution

    About Rs 69.3 crore of ARR, a burn multiple of 1.5 and about 18 months of runway. 42 x 1.65 is 42 plus 21 plus 6.3. A quarter's burn is 9.3, and 9.3 over 6.2 is 1.5 because both are multiples of 3.1. Cash of 55 over 3.1 a month is a shade under 55 over 3, so about 17.7 months.

    How do you multiply by 1.65 without a calculator?

    Break the awkward multiplier into pieces you already know. A shopkeeper adding 65% to a Rs 42 cost does not multiply by 0.65; he adds half, then a bit more. 65% is 50% plus 15%, so 42 x 1.65 is 42 plus 21 plus 6.3, which is Rs 69.3 crore. Fifteen percent is itself 10% plus half of that again: 4.2 plus 2.1. Every step is a halving or a shift of the decimal point, which is fast and hard to get wrong out loud.

    Why does the burn multiple need care before any arithmetic?

    Because the two inputs come in different periods. Burn is quoted per month and net new ARR per quarter. A burn multiple divides the cash burned by the new annual recurring revenue added over the same stretch of time, so three months of burn, Rs 9.3 crore, goes over the quarter's Rs 6.2 crore. Then notice that 9.3 is 3 x 3.1 and 6.2 is 2 x 3.1, so the ratio is exactly 3 over 2, or 1.5. Interviewers choose numbers like these on purpose; spotting the common factor is part of the test.

    Round first, then correct: three answers in under a minuteNext year's ARR42 x 1.65= 42 + 21 + 6.3(the base, half, then 15%)Rs 69.3 crBurn multipleQuarterly burn 3 x 3.1 = 9.39.3 / 6.2 = (3 x 3.1) / (2 x 3.1)(match the periods first)1.5Runway55 / 3 = 18.33.1 is 3% more than 3,so shave 3%: about 17.7~18 monthsThe slip: monthly burn over quarterly net new ARR, 3.1 / 6.2 = 0.5, looks three times better than it is.Both halves of a burn multiple must cover the same period.
    Splitting 1.65 into 1 plus a half plus 15% gives Rs 69.3 crore of ARR, matching periods turns the burn multiple into 9.3 over 6.2, which is 1.5, and rounding 3.1 down to 3 then shaving 3% gives about 17.7 months of runway.
    The relationship
    BM=3×3.16.2=1.5Runway=553.1≈17.7 months\text{BM} = \frac{3 \times 3.1}{6.2} = 1.5 \qquad \text{Runway} = \frac{55}{3.1} \approx 17.7 \text{ months}
    3 x 3.1net burn over one quarter, Rs crore
    6.2net new ARR added in the quarter, Rs crore
    55cash in the bank, Rs crore
    What it says in wordsPut burn and new revenue on the same period before dividing, and divide cash by monthly burn for runway.

    What do you say once the three numbers are out?

    Check them against each other, because that is what a growth investor does next. Growing ARR by Rs 27.3 crore next year needs about Rs 6.8 crore of net new ARR a quarter, a little above the Rs 6.2 crore just achieved, so the 65% plan is plausible but not banked. At a 1.5 burn multiple that growth costs about Rs 41 crore of burn in the year, and with Rs 55 crore of cash and about 18 months of runway, the company will want to raise again within roughly a year, before the runway gets short. That one sentence turns arithmetic into a view on the company.

    Where candidates lose it

    The costly slip is dividing the monthly burn by the quarterly net new ARR and announcing a burn multiple of 0.5. It makes the company look three times more efficient than it is, and the interviewer chose mixed periods to see whether you notice.

    The second loss is going silent while you calculate. Say the shortcut as you use it: half, then fifteen percent; three parts over two parts; fifty five over three, then shave a little.

    What the interviewer asks next

    • If net burn rises 20% next year while ARR grows 65%, what happens to the burn multiple if net new ARR grows in step with ARR?
    • How much cash should the company raise to have 24 months of runway at the current burn?
    • Is a burn multiple of 1.5 good for a company of this size, and what would change your view?

    Asked at Vista Equity Partners, Private Equity, Austin, 2021 (Wall Street Oasis): Mental math and tech/SaaS-specific sector insights

  2. 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.Mental maths and speed testsWarm upGeneral AtlanticNew York · 2026

    Try it first

    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 relationship
    (a−b)(a+b)=a2−b249×51=502−12=2,499998×1,002=1,0002−22=9,99,996(a - b)(a + b) = a^2 - b^2 \qquad 49 \times 51 = 50^2 - 1^2 = 2{,}499 \qquad 998 \times 1{,}002 = 1{,}000^2 - 2^2 = 9{,}99{,}996
    athe round number in the middle, 50 or 1,000
    bhow far each factor sits from it, 1 or 2
    a squared minus b squaredthe 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.
    Two shortcuts: a difference of squares, and one eighth50 x 50= 2,5005050bottom strip of 50moved up asa 1 x 49 stripon the right:49 x 51 = 2,500 - 149 x 51 = 2,499998 x 1,002 = 9,99,99612.5% = 1/8 of Rs 3,680 crore460eight equal blocksHalve three times:3,680all1,840half920quarter460eighth12.5% of Rs 3,680 crore = Rs 460 crore
    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.

  3. 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?Mental maths and speed testsWarm upVista 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.

    Blind guesses add 4 points for free when wrong answers cost nothingLeave 20 blank25.5 careful25.5Guess the last 2025.5 careful+429.501020304050Expected correct answers out of 50Time budget: 12 minutes / 50 questions = 14.4 seconds each. Save the last 30 seconds to fill blanks.
    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 relationship
    E[score]=30×0.85+20×15=25.5+4=29.5E[\text{score}] = 30 \times 0.85 + 20 \times \tfrac{1}{5} = 25.5 + 4 = 29.5
    30 x 0.85careful answers times your accuracy
    20 x 1/5blind 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.