Private Equity puzzles, solved step by step

Puzzles
100
Traced to a firm
22
Topics
12
Hard
30
Topic
All topicsCredit and PIK maths8Returns maths10Mental paper LBOs8Operating levers and margin maths8Valuation riddles10Fund economics numeracy9Market sizing and estimation9Compounding and time value7Mental maths8Probability and expected value in deals8Leverage and capital structure9Logic and brainteasers6
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–1 of 1 · filtered from 100Clear filters
  1. 085Without a calculator: what is 12.5% of 1,368 plus one third of 2,469?Mental mathsWarm upMid-market buyout fund

    Try it first

    Pick the answer before you work it.

    Show the worked solution

    994. Treat 12.5% as one eighth and halve 1,368 three times: 684, 342, 171. For a third of 2,469, split it into 2,400 and 69: a third of each is 800 and 23, so 823. Then 171 plus 823 is 994. Common percentages are fractions in disguise, and fractions are faster in your head.

    Why turn 12.5% into a fraction?

    Multiplying by 0.125 in your head means three digits of decimals to keep track of. Halving is something you have done since school, like splitting a restaurant bill between two, then four, then eight friends. 12.5% is exactly one eighth, so three halvings give the answer with no decimals at all. 1,368 halves to 684, then 342, then 171.

    12.5% is one eighth; a third is easier in friendly pieces12.5% = 1/8: halve three times1,368half684half again342half a third time1711/3: split into friendly pieces2,469split2,400 + 69a third of each800 + 23add the pieces823171 + 823 = 994
    Taking 12.5% of 1,368 is halving three times to 171, and a third of 2,469 is a third of 2,400 plus a third of 69, 800 plus 23, so 823; the two add to 994.

    How do you divide by three cleanly?

    Split the number into a part that divides easily and a small remainder. 2,469 is 2,400 plus 69, and a third of each is 800 and 23, so a third of the whole is 823 with no long division. Check it: 823 times 3 is 2,469. The same trick works for any divisor: pick the nearest round multiple, then handle the leftover.

    PercentageFractionHow to do it
    12.5%1/8halve three times
    16.7%1/6halve, then take a third
    33.3%1/3split into friendly pieces
    37.5%3/8an eighth, times three
    62.5%5/8half plus an eighth
    87.5%7/8the whole less an eighth
    Percentages that appear often in deal maths and the fractions they hide: each turns a decimal multiplication into halving or dividing by a small number.

    Buyout interviews use questions like this as a warm-up, often before a paper LBO, to see whether you will cope with arithmetic out loud. Saying each step lets the interviewer follow you and makes a slip easy to catch.

    Where candidates lose it

    The trap is attacking 0.125 times 1,368 as a decimal multiplication and losing a digit along the way, or rounding 2,469 to 2,500 and landing near 1,004. Both answers are close, which is exactly why they feel safe.

    Say the fraction first, one eighth, and the split, 2,400 plus 69. The interviewer hears a method and the arithmetic becomes easy.

    What the interviewer asks next

    • What is 37.5% of 2,496?
    • What is 87.5% of 640 minus one sixth of 1,242?
    • Why does knowing these fractions help when checking an IRR quickly?