Nobody fails a case because they cannot multiply seven by eight. Most of the math marks I have taken away, across several hundred scored cases, went to candidates who rounded $23.40 to $25 inside a margin, or lost a thousand between the units and the dollars, and never noticed the answer had moved by a fifth. A shortcut trades accuracy for time, and the price depends on the operation: close to free in a product, brutal in a subtraction. The interviewer is scoring whether you know which one you are in.
Most guides hand you a bag of tricks. This one gives you the price list, a way to size your rounding budget from the decision rather than from the numbers, and a break-even example in which nine cents decides the answer. By the end you should be able to say, before you start a calculation, where its error will come from, and round hard everywhere else.
What each operation charges for a shortcut
Physics labs teach this as propagation of uncertainty, and the rules fit on an index card: multiply or divide and percentage errors combine, add or subtract and absolute errors combine, raise to a power and the percentage error is multiplied by the exponent (Stony Brook physics lab guide). Labs combine random errors in quadrature, the formula in NIST's engineering statistics handbook; a rounding error has a sign you chose, so skip the quadrature, use the worst case, and add the percentages straight, with their signs.
| Operation | What rounding does | Check it yourself |
|---|---|---|
| Multiply | Percentage errors add | 380 × 0.23 = 87.4. Rounded to 400 × 0.25 = 100: a 5% and a 9% round became a 14% overshoot. |
| Divide | Percentage errors subtract | 2.1m ÷ 6.8 = 309k. Rounded to 2.1m ÷ 7 = 300k: 3% low. |
| Add | Errors dilute | 1.84m + 236k = 2.076m. Rounded to 1.8m + 250k = 2.05m: about 1% low. |
| Subtract two close numbers | Errors are multiplied by the larger number ÷ the difference | 23.40 − 19.10 = 4.30. Rounded to 25 − 20 = 5: a 7% and a 5% round became a 16% overshoot. |
| Compound over n periods | The rate's error is multiplied by n | 1.07^5 = 1.40. Rate rounded to 10%: 1.10^5 = 1.61, 15% high from a 2.8% round. |
Read the fourth row twice. Subtracting two close numbers is the only operation where a few percent of rounding moves the answer by tens of percent, and it sits behind every margin, contribution per unit, and gap to target in a case. The leverage is the larger number divided by the difference: 23.4 ÷ 4.3 is about 5.4, so a 1% slip on the price becomes a 5% slip on the contribution. Candidates learn shortcuts on multiplication drills and then spend them on margins. That is the whole problem in one sentence.
Ned's rule. Round before you multiply, never before you subtract. If the two numbers in a difference are within a factor of three of each other, carry every digit through the subtraction and round only what comes out.
Watch where case writers put the awkward digits. Bain's public Coffee Shop Co. practice case gives a £3 price, a £1 cost per cup, and fixed costs of £245,610 plus £163,740. The six-digit figures sit in the sum, where rounding is nearly free; the subtraction is 3 minus 1, and 410,000 ÷ 2 lands within 0.2% of the exact 204,675 cups. When the awkward digits sit inside the difference instead, $23.40 against $19.10, the difference is the test. In the cases I have written, that placement is deliberate.
Zeros before digits
The failure I mark most often is not arithmetic. In a first round of eight, I would expect one or two candidates to get a digit wrong and four or five to get a zero, a unit, or a per-what wrong. That is a tally from my own scoring sheets, not a study.
The fix: split every number into digits and a unit, and settle the units first. Name the unit of the answer, "dollars per year" or "units per store per week", then multiply the units, then the digits.
| Units you combine | Unit of the answer | Example |
|---|---|---|
| thousand × thousand | million | 40k units × $6k = $240m |
| thousand × million | billion | 12k stores × $30m = $360bn |
| million ÷ thousand | thousand | $18m ÷ 4k customers = $4.5k each |
| billion ÷ million | thousand, then the digits | $2bn ÷ 250m people: 2 ÷ 250 = 0.008, times a thousand, $8 a head |
If you ever get a trillion, you have picked up a stray unit: a $40m market at 15% share is $6m, and the candidate who writes 40m × 15m has lost track of which number is a percentage. Write the percent sign. Write "per year". Units are where case-room errors live, and the interviewer is listening for them.
Set the rounding budget from the decision, not from the numbers
Most guides say round to a friendly number, then adjust. Round to what the decision can afford. Every case calculation is a comparison against something: a break-even, a target margin, a competitor's price. Find the threshold before you compute, do one brutal pass to see how far away you are, then decide how carefully to do the second pass.
| Gap between rough answer and threshold | Rounding budget | What to do |
|---|---|---|
| More than 30% | Generous. One significant figure is fine. | Give the number, say which way you rounded, move to the so-what. |
| 10% to 30% | Modest. Two significant figures; round the factors of a product in opposite directions. | Give a range and say which side of it the truth sits on. |
| Under 10% | None inside any subtraction. | Carry the digits, say why you are slowing down, and finish with the sensitivity: how much one input must move to flip the answer. |
"Rough pass says about 360 against a threshold of 410, so I will be careful with the contribution" tells the interviewer you know where the risk is. It is also the fastest route through a case: most calculations land in the top row.
Worked example: nine cents decides the case
Lindqvist Outdoor, an invented Scandinavian maker of insulated bottles, wants to launch a 750 ml model. Price to retailers $23.40. Variable cost $19.10. Tooling and launch costs in year one $1.8m. Year-one forecast 410,000 units. Does it break even in year one?
Pass one, brutal, to find the gap. $25 minus $20, call it $5. $1.8m ÷ 5 is 360,000 units against a 410,000 forecast: a gap of about 12%, and both roundings pushed the contribution up, so the truth is worse. Middle row of the budget table, edging toward the bottom. The contribution has to be exact.
Pass two, careful where it counts. $23.40 minus $19.10 is $4.30, and nothing else; no rounding inside a difference. The division is a cheap place to round: anchor on $1.8m ÷ 4 = 450,000. The real divisor, 4.3, is 7.5% above 4, so take about 7.5% off 450,000: 34,000 off, call it 416,000. The exact figure is 418,605; the shortcut is 0.6% low, because dividing by 1.075 is not quite taking 7.5% off.
Pass three, the sensitivity, because the answer sits within a few percent of the line. Ten cents of contribution is 2.3% of $4.30, so it moves break-even by roughly 10,000 units. Breaking even at exactly 410,000 units needs a contribution of $1.8m ÷ 410,000, which is $4.39. Nine cents.
| Pass | Contribution | Break-even | Against the 410,000 forecast | Verdict |
|---|---|---|---|---|
| Brutal: 25 − 20 | $5.00 | 360,000 | 50,000 over | Launch |
| Careful: exact subtraction, rounded division | $4.30 | about 416,000 | about 6,000 short | Marginal |
| Exact | $4.30 | 418,605 | 8,605 short | Marginal, nine cents from viable |
What you say: "I kept the subtraction exact because the two numbers are close, and rounded the division, which puts me inside one percent on the low side. Break-even is a shade above the forecast, so year one is roughly flat, about $37,000 short. Before I say no: a dime of price, or a dime off freight, flips it."
The brutal pass would have said "launch, comfortably": wrong in direction, wrong in size, and blind to the only insight in the case, that the launch is a ten-cent negotiation.
The kit, ranked by how often I ask for it
You do not need twenty tricks. Four cover most rooms, each paired with its cost, in roughly the order they come up; the order is my estimate, not published data.
| Operation | Shortcut | What it costs |
|---|---|---|
| Percent of a number | Build from 10%, 5%, and 1% blocks: 23% of $6.4m is 640k + 640k + 192k = $1.47m | Nothing; it is exact. The risk is the base, not the arithmetic |
| Rate × base | Round the two factors in opposite directions: 380 × 0.23 becomes 400 × 0.22 = 88, against 87.4 | Under 1% if the rounds oppose; the sum of both if they agree |
| Division | Move the divisor to one that goes in cleanly, then adjust by the percentage you moved it, sign flipped: $4.1m ÷ 7.2 becomes $4.2m ÷ 7 = 600k, less about 5% for the two nudges, so 570k against 569k | Only the adjustment, which you can state |
| Compounding | For n × g under 30%, growth is about n × g plus a tenth of it: 6% for four years is 24% plus 2.4, about 26%, against 26.2%. Doubling time is about 72 ÷ g | The rate's rounding times n, so never round the rate |
Nothing in the middle column is secret. The right-hand column is what the interviewer grades.
What the interviewer writes down while you are rounding
None of the firms says "get the exact number". BCG's interview preparation brochure says the calculations will be simple and, "rather than testing computational skills, this is meant to see if you can use numbers to quickly form opinions and guide decisions." Bain's case interview page says "Think aloud: Share your reasoning and calculations, even if you're unsure." McKinsey's Beautify practice case says calculators are not allowed, write the calculation on paper, and "Don't feel rushed into performing calculations. Take your time."
On the sheets I have used, the number itself is one box. The boxes beside it ask whether the setup came before the digits, whether the candidate said what the number meant, and whether I had to rescue them. A candidate who lands 3% high and says "3% high, because I rounded the price up" fills the approach box and, in practice, the accuracy box too. A candidate who lands exactly right and cannot say whether that is good news fills one box.
So the narration has three beats: direction, size, so-what. "Rounded both up, so this is a ceiling. True number is a few percent lower. Either way we clear the target by a third." Ten seconds, and the interviewer stops worrying about your arithmetic.
Practice this today
One assignment, fifteen minutes. Take any three-number problem, a price times a volume minus a cost, or a fixed cost divided by a margin. Solve it three ways: brutally rounded, rounded with the factors pushed in opposite directions, and exact. Before checking each, write down the sign and rough size of the error you expect. You are training the prediction, not the speed; a candidate who can say "about 5% high" has done the interviewer's checking for them.
CoachNed's quick math drill is free forever and serves a fresh problem every rep; the graded math drill scores the setup and the narration, not only the digit. Everything on the site is open for seven days with no card; after that it is $120 for a recruiting season or $49 a month.
CoachNed is independent and not affiliated with McKinsey, BCG, Bain, or any other firm named here.
Frequently asked questions
Are calculators allowed in case interviews?
Not at the firms that say anything about it. McKinsey's practice cases state that calculators are not allowed, and its assessment integrity page lists a calculator alongside generative AI and prepared notes as things to refrain from. Assume pen and paper unless your invitation says otherwise.
How accurate does case interview math need to be?
As accurate as the decision requires, which you learn from a rough pass. More than 30% from the threshold, one significant figure with a stated direction is enough; inside 10%, carry the digits through any subtraction and finish with the sensitivity.
Should I round up or down in case math?
Round in the direction that makes the answer conservative for the decision, and say which way you went. In a product, round the two factors in opposite directions so the errors cancel; in a subtraction of two close numbers, do not round at all.
Sources
- McKinsey, Beautify practice case — no calculators, write calculations on paper, do not feel rushed. Checked 2026-09-24.
- McKinsey, Assessment Integrity Expectations — no calculator, generative AI, or prepared notes in any assessment or interview. Checked 2026-09-24.
- BCG, Interview Preparation brochure (November 2018) — calculations test whether you can use numbers to form opinions, not computational skill. Checked 2026-09-24.
- Bain, Preparing for the Case Interview — think aloud, share calculations even when unsure, emphasize key numbers. Checked 2026-09-24.
- Bain, Coffee Shop Co. practice case — the £3 price, £1 cost, £245,610 and £163,740 fixed costs, and 204,675-cup break-even. Checked 2026-09-24.
- Stony Brook University Physics, Guide to Uncertainty Propagation and Error — relative errors combine in products and quotients, absolute errors in sums and differences, powers multiply the relative error by the exponent. Checked 2026-09-24.
- NIST/SEMATECH e-Handbook of Statistical Methods, propagation of error — the standard formulas for how uncertainty in inputs carries into sums, differences, products, and quotients. Checked 2026-09-24.
- BCG Careers, Case Interview Preparation — BCG's current guidance: "perform quick calculations" and "there isn't always a single right answer." Checked 2026-09-24.