The math in a case interview is never hard — it is just asked fast, out loud, while someone watches. This free lesson rebuilds the six formulas that carry almost every case — percent change, the business equation, margin, breakeven, payback and sizing, funnel and mix — each one landing on the page line by line: the terms first, then the worked substitution, then the result, exactly the way you should write it on your page in the room. No algebra background needed; the point is order, not cleverness. Read it signed-out, then warm up your arithmetic on our free mental-maths drill.
Start the free lesson → Warm up on the maths drill → Chapter: 4 · Exhibits and numbers · Format: interactive, reads like a lesson · Cost: free, no card A sample of the first worked equation in this lesson, shown as it builds in the lesson. /learn · a sample of the lessonWorked equation
Explore phase
Start this lesson →One phase, six worked equations: every formula is a step-revealed build — terms, substitution, result — the same order your page should follow in the interview.
MovementPercent change done honestly: absolute change first, percent second, and the materiality check that stops you charting noise.
The engineThe business equation, margin and breakeven — the three that answer “does this make money?” — each worked on the same gym case.
The lensPayback and sizing, then funnel and mix — the formulas that turn a hunch (“the discount is costing us”) into a number.
The other free lessons: How a case unfolds → Case interview frameworks →Case interview math is not hard math. It is a short list of business calculations, done quickly, out loud and without mistakes, then turned into a sentence about what the number means. These are the ones the lesson works through, each with a worked example.
Percent change is the change divided by the starting value. Revenue that moves from £80 million to £92 million has risen by £12 million, which is 12 ÷ 80, or 15%. Always state both the absolute and the percent change, then say whether it matters: a 15% rise in a cost that is 2% of the total is not where the problem lies.
With numbers: a café sells 50,000 coffees a year at £3, so revenue is £150,000. If each coffee costs £1 to make and fixed costs are £60,000, profit is £150,000 − £50,000 − £60,000 = £40,000, a margin of about 27%. The first question in most cases is which of those numbers changed.
Contribution is what each unit adds after its variable cost: price minus variable cost. The café’s contribution is £2 a coffee. Break-even volume is fixed costs divided by contribution: £60,000 ÷ £2 = 30,000 coffees. Selling 50,000 leaves a cushion of 20,000 coffees, or 40% of volume, before the café loses money. Use the same relationship whenever a new cost or a price change comes up.
Payback is the investment divided by the annual profit or saving it brings. A £2 million machine that saves £500,000 a year pays back in four years. Return on investment is the annual gain divided by the investment, here 25%. Compare either with the bar the client sets, if the brief gives one; if not, ask.
Growth compounds. A business growing 10% a year for three years grows by 33%, not 30%, because 1.1 × 1.1 × 1.1 is 1.33. To estimate how long something takes to double, divide 72 by the yearly growth rate: at 8% a year, about nine years. Declines compound the same way, so two years of 10% decline is a 19% fall.
Build a chain of estimates from something you know. For a market in UK gym memberships: about 67 million people, perhaps 15% belong to a gym, at about £35 a month, gives 10 million members × £420 a year, or about £4 billion. Round at each step, say each assumption aloud, and finish by saying whether the answer is big enough to matter to the client.
A funnel multiplies conversion rates. If 200,000 people visit a website, 40% reach the sign-up page and 5% of those sign up, that is 4,000 new customers. Multiply by first-month profit per customer to value the funnel, and compare the drop at each stage, because a fix earns most where the drop is sharp.
An average across groups must be weighted by the size of each group. If 80% of sales earn a 10% margin and 20% earn a 40% margin, the average margin is 0.8 × 10% + 0.2 × 40% = 16%, not the 25% a simple average gives. This trap is common in exhibits that show margins by product or region.
The lesson teaches the formulas; the site’s free mental-maths drill builds the speed, and the BCG Quantitative Reasoning Test guide has worked questions at test pace. Case Ace’s Case Math and Guesstimate drills then mark your working step by step — 221 drills across 45 lessons, alongside 46 AI-run cases.
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