Investment Banking puzzles, solved step by step

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100
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All topicsProbability7Mental maths and counting11Growth and compounding9Valuation riddles11Logic and brainteasers11Rates, risk and options9Estimation and market sizing7Accounting riddles9Expected value and games7Enterprise value and dilution6Deal maths6DCF and cost of capital7
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Showing 1–2 of 2 · filtered from 100Clear filters
  1. 005A stock falls 10% one day. How much does it need to rise the next day to get back to where it started?Mental maths and countingWarm upJefferiesLondon · 2026

    Try it first

    Pick the answer before you calculate.

    Show the worked solution

    About 11.1%. A price of 100 falls 10% to 90. Getting back to 100 needs a rise of 10 on a base of 90, which is 10 divided by 90, or 11.1%. The general rule: to recover a loss of L, you need L divided by (1 minus L), which grows much faster than the loss itself.

    Why is the recovery bigger than the fall?

    A 10% discount on a 100 rupee shirt takes it to 90. If the shop then marks it up by 10%, the tag reads 99, not 100, because the markup is taken on 90. Percentages are always measured against a base, and after a fall the base is smaller, so the same rupee gain is a bigger percentage.

    The same 10 rupees is a bigger percentage of a smaller base100Day 090Day 1100Day 2Fall: -10 = 10% of 100Climb back: +10 = 11.1% of 90if gain = loss10% loss needs 11.1%30% needs 42.9%50% needs 100%Loss sufferedGain needed0%25%50%
    A fall from 100 to 90 is 10%, but the climb from 90 back to 100 is 11.1% because it starts from a smaller base. The gap widens with the size of the loss: 30% needs 42.9% to recover and 50% needs a full 100%.
    The relationship
    g=L1−L0.100.90=11.1%g = \frac{L}{1-L} \qquad \frac{0.10}{0.90} = 11.1\%
    Lthe loss, as a decimal
    gthe gain needed to get back to the start
    What it says in wordsThe gain needed to recover equals the loss divided by what is left after the loss.

    What do you add to sound like a banker rather than a calculator?

    Give the number, then the pattern. Large drawdowns are hard to climb out of: a fund that loses 50% has to double just to break even. That one sentence shows you see why lenders and investors care about downside, which is the real reason the question is asked.

    Where candidates lose it

    Saying 10% is the whole trap, and it happens because the question is asked fast and sounds symmetric. The interviewer wants to see you notice the base changed.

    If you say 11% rather than 11.1%, that is fine; say 10 over 90 so the method is audible.

    What the interviewer asks next

    • A stock rises 50% and then falls 50%. Where does it end?
    • Two days of minus 10% and plus 10%: are you up or down, and by how much?
    • Why does this matter for how a fund reports its drawdowns?

    Asked at Jefferies, Generalist (IBD spring week), London, 2026 (Wall Street Oasis): if a stock goes down 10% one day how much does it need to go up by the day after to get back

  2. 100Online numerical test style: three divisions had revenue of Rs 420, 260 and 120 crore last year and Rs 462, 299 and 150 crore this year. Which division grew fastest, and which contributed most to the growth in total revenue?Mental maths and countingWarm upBarclaysNew York · 2026

    Try it first

    Which division contributed most to total growth?

    Show the worked solution

    Division C grew fastest, at 25%, but Division A contributed most, adding Rs 42 crore of the Rs 111 crore increase. Growth rates are 42/420 = 10%, 39/260 = 15% and 30/120 = 25%. Rupee increases are 42, 39 and 30. A's slower rate on a much bigger base adds more. Total revenue grew 13.9%, and A supplied 37.8% of that growth.

    Why are these two different questions?

    A child's pocket money rising from 100 to 150 is 50% growth; a parent's salary rising from 1 lakh to 1.1 lakh is 10%. The household budget still cares far more about the salary. A growth rate measures change relative to each part's own size; contribution measures change in rupees, which is what adds up to the total. Online tests ask both in one question because candidates who rush answer the same division twice.

    Two questions, two columns: growth rate and rupee increaseDivisionLast yearThis yearGrowthIncreaseadded by youDivision A42046210%+42Division B26029915%+39Division C12015025%+30Total80091113.9%+111Rs crore. Lime cells answer the two questions asked.1Fastest growth: C, 25%on the smallest base2Biggest contributor: A, +4237.8% of the total rise3Total grew 13.9%not the 16.7% simple average
    Adding a growth column and an increase column to the table shows Division C growing fastest at 25% while Division A adds the most, Rs 42 crore or 37.8% of the Rs 111 crore rise, and total revenue grows 13.9%.

    How do you do it fast under a timer?

    Compute the increases first, because they are subtractions: 42, 39, 30. Then compute rates only where needed, using easy fractions: 42 on 420 is a tenth, 30 on 120 is a quarter, 39 on 260 sits between them at 15%. Write the two added columns next to the table rather than holding the numbers in your head, because the next question in the set often reuses them.

    The relationship
    gtotal=∑iwi gi=420800(10%)+260800(15%)+120800(25%)=13.9%g_{\text{total}} = \sum_i w_i\, g_i = \tfrac{420}{800}(10\%) + \tfrac{260}{800}(15\%) + \tfrac{120}{800}(25\%) = 13.9\%
    w_ieach division's share of last year's revenue
    g_ieach division's growth rate
    What it says in wordsTotal growth is the average of the divisions' growth rates weighted by their starting size.

    That weighting is the third trap a test can set. The simple average of 10%, 15% and 25% is 16.7%, which is wrong because it gives the small division the same say as the large one. Total revenue went from 800 to 911, a rise of 13.9%. If an option shows 16.7%, it is there to catch exactly that shortcut.

    Where candidates lose it

    The trap is answering C to both parts, because the 25% is the most striking number on the page. The test separates fast readers from careful ones by asking for two different measures in one question.

    The second loss is averaging growth rates to get total growth. Always weight by size, or simply add the totals and compute once.

    What the interviewer asks next

    • If Division C keeps growing 25% and A keeps growing 10%, in how many years does C add more rupees than A?
    • What share of total revenue will each division have next year if growth rates repeat?
    • How would you present these numbers on one slide for a client?

    Asked at Barclays, Investment Banking, New York, 2026 (Wall Street Oasis): The numerical section involved interpreting tables and charts quickly