Case interview maths: the calculations that actually come up

What is case interview maths actually testing?

The most useful thing to know about case interview maths is that the arithmetic is easy. There is no calculus, no statistics, no matrix algebra, nothing you did not meet by about the age of fifteen. Percentages, ratios, multiplication, division, a little compounding. Sat on paper, alone, in silence, you would get almost all of it right.

What makes it hard is the setting. You are dividing 4.2 million by 35,000 out loud, in front of someone who is writing, while holding in your head what the number is for and what you promised to do with it next. The pressure does not make the sums harder. It makes you drop things: a unit, a zero, which of the two figures was annual and which was monthly.

On our rubric, quantitative work is marked under rigor, one of fourteen skills across three dimensions, each scored 1 to 5 with 3 meaning you met the first-round standard. What rigor rewards is worth spelling out, because it is not simply the right answer. It rewards three things: an auditable chain, assumptions stated as assumptions, and a sense-check at the end.

Why an audible slip is cheap

Auditable means an interviewer could reconstruct your working from what you said. You name the figures you are using, you say what you are doing to them, and you say each result before you use it in the next step. That is what makes an arithmetic slip cheap. If you divide wrong at step three but the interviewer heard steps one and two, your approach is on the record and scoreable, and either they catch the slip or your own sense-check does.

Two failure modes cost a great deal. The first is silent maths: thirty seconds of pen movement, then a number. There is nothing to mark. If the number is right, the interviewer cannot tell whether you understood the problem; if it is wrong, they cannot tell where it went wrong. The second is a confident wrong answer with no sense-check. Reporting that a regional grocer's addressable market is £900 billion, in the same tone you would use for £900 million, says something worse about your commercial judgement than a wrong number says about your arithmetic.

The sense-check is the third element, and the one most often omitted, partly because nobody tells candidates what it is. It is not re-doing the sum. It is comparing the answer to something that came from outside the calculation: a figure the client already gave you, a market you happen to know, or a per-head or per-store number you can judge by eye. "That works out at £1,200 per household per year on groceries, which looks low for a family of four" is a sense-check. "Let me just check my arithmetic" is not.

Stating assumptions is the cheapest mark on the page and the most often skipped. A number you invented is fine as long as you label it as invented: "I'll assume an average basket of £30, and I'll flag that as the figure I would want to check first." The same number delivered as fact reads as a guess dressed as data, and it invites exactly the follow-up question you did not want.

Which calculations do you need to know cold?

Across the transcripts we mark, the same calculations keep reappearing. Not because interviewers lack imagination, but because commercial problems have a small number of shapes: is this worth doing, at what volume does it pay for itself, how fast is it growing, and what does the business actually earn per unit.

Below are the eight worth holding at reflex level. Know each well enough that you are not deriving it in the room, because the derivation is where the clock and your working memory both go.

Two of these deserve a warning label. Percentage points is where candidates give away free marks. If a margin moves from 8% to 10%, that is a rise of two percentage points and an increase of 25%, because 2 divided by 8 is 0.25. Both numbers are true and they answer different questions, so say which one you mean.

CAGR is the other. The n in the exponent is the number of intervals, not the number of data points. Revenue in 2022 growing to revenue in 2026 is four years of growth, even though five years are named on the chart. Interviewers notice this one, because getting it wrong quietly distorts every forecast built on top of it.

Weighted average is the quiet one. Handed two segment margins, candidates average them and move on. If one segment turns over £100m at a 40% margin and the other £300m at 20%, the blended margin is not 30%. It is (100 × 0.40 + 300 × 0.20) ÷ 400, which is £100m of margin on £400m of revenue, so 25%. Five percentage points of error, and it is always the large low-margin segment that gets under-weighted. Whenever you are given two percentages and asked for one, establish the weights before you combine them.

How much volume can you lose on a 10% price rise?

Pricing questions produce the single most common wrong answer in case interviews, and it is wrong in a revealing direction. Asked how much volume a business can afford to lose after a 10% price rise, most candidates say something close to 10%. The true figure at a healthy contribution margin is meaningfully lower, and understanding why is worth more than memorising the formula.

Take a product priced at £100 with a 60% contribution margin: £60 of every sale covers fixed costs and profit, and £40 goes on variable cost. Management raises the price by 10%. Fixed costs do not change, and neither does the variable cost per unit, because making the thing costs what it cost. So the whole of the £10 increase drops straight into contribution.

The direction of the answer is the part to internalise. A price rise buys more headroom than intuition suggests, and the thinner the contribution margin, the more headroom it buys. Run the same calculation at a 20% margin and the tolerable loss is 0.10 ÷ 0.30, or 33%. Run it at a 90% margin and it is 0.10 ÷ 1.00, or 10%. Low-margin businesses are the ones with the most to gain from price and the least to gain from volume, which is usually the insight the case was built to produce.

Price cuts run the same way with one sign flipped: required volume gain = price cut ÷ (contribution margin - price cut). Cutting a 60% margin price by 10% needs 0.10 ÷ 0.50, so 20% more volume just to stand still. Cutting a 20% margin price by 10% needs 0.10 ÷ 0.10, which is 100%: you have to double the business to fund the discount. That is the arithmetic behind why discounting is so often the wrong answer, and it is a better thing to say than "discounting can be risky".

How do you do growth and CAGR without a calculator?

Growth arithmetic appears in almost every market-facing case, in two forms: compounding a run of annual rates into a total, and turning a start figure and an end figure into one annual rate. Both are doable in your head, provided you accept a small error and declare it.

The additive shortcut is safe when the rates are small and the periods are few. The error is roughly the sum of the pairwise products, so three years at around 10% costs under two percentage points, which no interviewer will object to once you have named it. It stops being safe quickly, though. Five years at 20% a year compounds to 1.2 to the fifth power, which is 2.49 times the starting size, or 149% growth, where adding the rates gives 100%. At that point the shortcut is not an approximation, it is a wrong answer.

The rule of 72 is the other honest shortcut. Divide 72 by the annual growth rate as a whole number and you get the years to double. It is accurate enough to say out loud for rates between roughly 4% and 15%, and it drifts outside that band: at 1% it gives 72 years against a true 70, and at 25% it gives 2.88 years against a true 3.11. Inside the band the error is small enough that the rounding in your inputs dominates it.

Running it backwards is just as useful and much less commonly done. If a client says the market has doubled in six years, that is 72 ÷ 6, so about 12% a year. The true figure is 12.2%. Nobody in the room will mind, and you have converted a vague statement into a rate you can now forecast with.

How do you do arithmetic out loud without falling over?

Everything above is the easy half. The hard half is executing it out loud, at conversational pace, without losing the thread. Five habits do most of the work, and they are habits rather than tricks: they have to be installed in practice, because under pressure you do what you have rehearsed rather than what you intended.

One structural point sits underneath all five. Divide your page before the case begins: a wide column for the working, a narrow one down the right for assumptions and for figures the interviewer hands you. Numbers you were given and numbers you invented should never share a column, because when you are asked where the £30 came from, you want to point at it rather than reconstruct it. It also means you never mislay a figure and have to ask twice for the same one.

One more thing, and it removes more anxiety than any technique on the list. Asking for a figure to be repeated is not a deduction. It never has been. Numbers are stated once, out loud, frequently over a video call with half a second of lag. Asking again is what a competent colleague does, and if an interviewer bothers to write a note about it at all, it goes under listening as a positive. What genuinely costs you is guessing at a figure you did not catch and then building three steps of analysis on top of it.

How do you practise until it is reflex under pressure?

Case maths is closer to a motor skill than a body of knowledge, which means the practice that works looks unlike revision. You are not trying to learn the formulas. You are trying to make retrieval automatic, so that your working memory is free for the commercial thinking that the maths is only there to serve.

Short daily reps beat long weekend sessions

Fifteen minutes a day for three weeks builds more fluency than three long weekend sessions, and it builds it in fewer total hours. The skill you want is fast recall under load, and recall responds to frequency far more than to duration. If you only have an hour a week, spend it as four separate fifteen-minute blocks rather than one sitting.

Do them out loud, standing up

This sounds like a gimmick and is not. Silent practice trains a different skill from the one being assessed: you can do a calculation on paper perfectly and still stall the first time you have to narrate it. Speaking the working uses the same channel you will use in the room, and it exposes the specific things that collapse under vocalisation, which are almost always units and place values. Standing adds the low-grade physical stress that makes the rep resemble the event.

Finish every rep with a sense-check sentence

Make it a rule that no calculation is finished until you have said one sentence comparing the answer to something outside it: a market you know, the client's current figure, a per-head or per-store number. This is the single habit that most reliably moves rigor from a 3 to a 4. Practise it on sums whose answers you already know, so the sentence becomes automatic rather than something you produce only when you happen to have spare capacity.

Write the assumption next to the number

In practice, and then in the room, put the assumption in the margin beside the figure it produced: "basket £30, assumed", "two visits a week, assumed". Two things follow. You never present an invented number as data by accident, and when the interviewer pushes on one of your inputs, you can see immediately which parts of the answer move. That is usually the question they were really asking.

Build the rep bank out of cases rather than out of a mental-arithmetic app. Take a calculation you have already met, change the inputs, and redo it out loud from the set-up: the same breakeven at a 35% margin instead of 60%, the same market sizing on a different population. Random arithmetic drills train the digits. Recycled case calculations train the digits and the framing together, and it is the pairing that transfers into the room.

If you want reps that are marked rather than self-assessed, the 100 drills at /drills include timed maths reps scored by AI against the same rubric anchors an interviewer uses, so you get a rigor score and the line where the chain broke instead of a tick or a cross. The coaches are AI personas built by ex-MBB interviewers, and they are always disclosed as AI. The first full case is free.