An elegant structure, good intuition about the industry, then an error by a factor of ten in a market-size calculation: the case collapses. Interviewers know it, and many consider that an undetected calculation error weighs more heavily than an imperfect structure. Mental arithmetic is not a display of virtuosity; it is the ability to handle orders of magnitude accurately, under pressure, and to do so out loud. This article gathers the techniques that hold up in interview, with examples drawn from typical cases, and proposes a short practice routine.
What the interviewer expects from your calculations
Firms are not looking for human calculators. Boston Consulting Group writes on its case interview preparation page 🔗 that the candidate must, among other things, analyse data and perform quick calculations to identify the most important factors. Its page on the process in German-speaking offices specifies that calculations serve to check that the candidate can quickly draw a conclusion from them, that they must be accurate and integrated into the reasoning, and recommends practising mental arithmetic before the interview.
Three expectations emerge:
- accuracy: the result must be correct, at least in order of magnitude, with rounding you own up to;
- reasonable speed: no rushing, but no long minutes of silence either;
- interpretation: each figure obtained must be linked to the question of the case. “The market is worth about 400 million” is not enough; “the market is worth about 400 million, so the target of 100 million in revenue implies a market share of a quarter, which seems ambitious” answers the case.
This third point is the one candidates forget most often. A correct but uninterpreted calculation earns almost nothing.
Rounding without losing accuracy
Rounding is the main tool of mental arithmetic in interview. Use it boldly, but announce it.
Round the starting data. A population of 67.8 million becomes 70 million, a price of €4.85 becomes €5. Say so: “I am rounding the population to 70 million to keep things simple.”
Offset your rounding. If you round one factor up, round the next one down when possible. 68 × 4.8 gives roughly 70 × 4.7, about 330; the exact calculation gives 326.4.
Keep two significant figures. In interview, 330 is enough; 326.4 adds nothing. But 300 may be too rough if the conclusion depends on a nearby threshold.
Check the effect of rounding on the conclusion. If the decision depends on a gap of a few per cent, redo the calculation more precisely. If it does not, carry on.
Powers of ten for large numbers
Errors by a factor of ten or a thousand almost always come from large numbers: millions, billions, multiplications between populations and prices. Powers-of-ten notation eliminates them.
The method consists of splitting each number into a simple figure and a power of ten, multiplying the figures on one side and the powers on the other.
Example. A case asks for the size of the French market for gym memberships. You set out: 30 million adults of an age to subscribe, a subscribing share of about 15%, an average membership of €40 a month.
- 30 million = 3 × 10⁷
- 15% = 1.5 × 10⁻¹
- €40 × 12 months = €480, rounded to €5 × 10²
Product of the figures: 3 × 1.5 × 5 = 22.5. Product of the powers: 10⁷ × 10⁻¹ × 10² = 10⁸. Result: 22.5 × 10⁸ = 2.25 × 10⁹, or about 2.2 billion euros a year.
These assumptions are those of an exercise; in interview, the interviewer will tell you whether they are reasonable or give you theirs. The value of the method lies elsewhere: you never get lost in the zeros.
A useful benchmark: memorise a few common orders of magnitude so you can set your assumptions quickly (a country’s population, the number of households, the length of a year in days and hours), and check them regularly against public sources such as France’s national statistics institute Insee, rather than memorising figures from forums.
Percentages, growth and margins in your head
Profitability and growth cases rely on a few recurring calculations, each of which has a shortcut.
Percentages as fractions. 25% = a quarter, 20% = a fifth, 12.5% = an eighth, 33% ≈ a third. 12.5% of 640 is calculated faster as 640 / 8 = 80.
Percentages by decomposition. 17% of 300 = 10% (30) + 5% (15) + 2% (6) = 51.
Successive changes. A 10% rise followed by a 10% fall does not bring you back to the starting point: 1.1 × 0.9 = 0.99, a 1% fall. For small changes, rates can be added as a first approximation: +3% then +4% give about +7%.
Compound growth and the rule of 72. An amount growing at r% a year doubles in about 72 / r years. At 8% a year, it doubles in about 9 years; at 6%, in 12 years.
Margins. If a company makes 200 in revenue and 30 in profit, its margin is 30 / 200 = 15%. If costs rise by 10% and prices stay flat, profit becomes 200 − 170 × 1.1 = 200 − 187 = 13, a margin of about 6.5%. This kind of calculation illustrates the leverage effect of costs on margin, a useful reflex in the profitability case.
Break-even. Fixed costs / unit margin. With 1.2 million in fixed costs and a margin of 30 per unit sold, you need to sell 40,000 units to cover costs.
Talking it through to avoid mistakes
In interview, mental arithmetic is done out loud. It is a constraint, but also a protection.
Announce the method before calculating. “I will multiply the number of households by the ownership rate, then by the average price.” The interviewer can correct an assumption before you waste time.
Write down the steps. Note each intermediate result on your sheet, with its unit. Most mistakes come from a forgotten unit (months versus years, thousands versus millions).
Do a plausibility check. Before announcing the result, ask yourself whether it is plausible. A national bakery market of a few million euros, or a hair salon serving ten thousand customers a day: these results should stop you.
Acknowledge a mistake straight away. If you make a mistake and see it, say so and correct it: “Let me start again, I forgot to multiply by twelve months.” A mistake you correct yourself weighs much less than one the interviewer has to point out.
Conclude on the meaning. Each calculation ends with a sentence saying what it changes for the question asked.
Practising every day in a short time
Mental arithmetic improves quickly with regular, short practice, much better than with long occasional sessions.
- Ten minutes a day for three weeks, with varied exercises: two-digit multiplications, divisions, percentages, conversions.
- Case calculations rather than abstract ones: each day, estimate a market, a capacity or a cost based on a news story.
- Out loud, with a sheet of paper, as in interview.
- With a partner who plays the interviewer and interrupts you, to get used to calculating while someone watches.
The online tests used by some firms also rely on reading figures quickly; our article on consulting firms’ online tests describes these formats. And on how calculation fits with structure, the article on case interview frameworks points out that each calculation must serve a branch of the tree.
Quantitative ease also shows on a CV: a forecasting project, a model built during an internship, a data tool used. The strategy consultant CV template thus highlights ownership of the Excel model on each engagement. The ConseilCV editor lets you concentrate on this evidence: it handles the layout and outputs a PDF that screening software reads without difficulty.
Frequently asked questions
Are you allowed a calculator in a case interview?
Generally not during case interviews. Some online tests allow it, others forbid it: check each firm’s instructions.
What if you get stuck on a calculation?
Simplify: round more, break the calculation into smaller steps, and say what you are doing. The interviewer prefers a correct order of magnitude reached step by step to a prolonged silence.
Should you know figures by heart?
A few orders of magnitude are useful (population, households, number of working days), but the interviewer accepts reasonable assumptions, especially if you state them. They will correct them if necessary.
Does mental arithmetic count for non-quantitative profiles?
Yes. Firms expect a minimum of ease with numbers from every candidate, whatever their background. It is one of the skills that improves fastest with practice.
Sources
- Boston Consulting Group, Case interview preparation 🔗
- Boston Consulting Group, Bewerbung und Interviews 🔗
- McKinsey & Company, Interviewing at McKinsey 🔗
- Insee, statistics and studies 🔗