Case Interview Math 2026: How to Practice and Get Fast

What case interview math is and what it covers

Case interview math is the unaided arithmetic you work out loud inside a case: multiplication, division, percentages, ratios and growth rates applied to business figures. Nothing harder is tested. There is no algebra beyond a single linear equation, no calculus and no statistics.

What gets assessed is speed and reliability without a calculator, plus the reading you give the number once you have it. The difficulty of the operation is almost never the point. A candidate who divides 409,350 by 2 in four seconds and then says what 204,675 means for the client has done the whole task.

Bain publishes the rule that draws the line, at bain.com: a calculator is allowed on its 30 to 40 minute digital assessment and ruled out in the interviews that follow. Page checked 29 September 2026. The two halves test different things. The assessment delegates execution to a machine and watches your judgment. The live case watches the execution too.

The clock is published as well. Accenture's case workbook, read as a PDF on 29 September 2026, states that interviews run 45 to 60 minutes, with 30 to 45 minutes on the case itself. Thirty seconds lost recovering a slipped decimal comes out of that window.

Interpretation carries its own weight. A number with no sentence attached is an unfinished answer. A Kearney business analyst puts the rule plainly on her employer's blog, read at kearney.com on 30 September 2026: "When you're working through the quantitative part of the case, you should never end on a number."

The case interview math topics firms test

Four topics carry almost every calculation in a case, and they arrive in this order: profitability, break-even, growth rates, market sizing.

Profitability. Profit is revenue minus cost, revenue is price times volume, and a margin is a profit divided by a revenue. Most profitability cases are a subtraction wrapped in two multiplications, then a comparison of two margins.

Break-even. Fixed costs divided by the unit contribution margin gives the volume at which profit is zero. Bain publishes one worked end to end in its coffee case: a three pound cup with one pound of variable cost gives a two pound unit margin, costs of 163,740 and 245,610 pounds add to 409,350 pounds, and 409,350 divided by 2 is 204,675 cups. Against a market of 7,000,000 cups that is 2.9 percent, which the firm rounds to about 3 percent. Recomputed by hand, page checked 29 September 2026. The firm charges the full opening cost against the first year, and that convention moves the answer, so ask for it. More on the structure sits on break-even analysis.

Growth rates. A growth rate is the change divided by the old value. Compounding over several years needs a power, and the shortcut for it is below.

Market sizing. A sizing is a chain of multiplications and one division, usually population to households to penetration to frequency to price. Accenture's workbook publishes a dry cleaning sizing that ends by dividing one million units by a capacity band: 1,000,000 over 4,800 is 208.3 and 1,000,000 over 3,200 is 312.5, which is the published answer of 208 to 312 outlets. We recompute that final step and leave the earlier steps to the document, because our reading of the PDF does not reconstruct them.

The business formulas worth knowing by heart

Nine equations cover the arithmetic of a case. Each one is short enough to say out loud, and together they close every topic above.

1. Profit = revenue minus total cost.
2. Revenue = price times volume.
3. Gross margin percent = (revenue minus cost of goods sold) divided by revenue.
4. Operating margin percent = operating profit divided by revenue.
5. Unit contribution margin = price minus variable cost per unit.
6. Break-even volume = fixed costs divided by unit contribution margin.
7. Market share percent = our volume divided by total market volume.
8. Growth rate percent = (new value minus old value) divided by the old value.
9. Payback period in years = upfront investment divided by annual cash return.

Two of them do more work than the rest. Equation 5 is the one candidates skip, and every break-even, pricing and volume question runs through it. Equation 8 has a trap in the denominator: a growth rate measured against the new value instead of the old one understates every increase.

Three further equations appear in finance-flavored cases: return on investment, a perpetuity as a cash flow divided by a discount rate, and working capital as receivables plus inventory minus payables. They are worked with numbers on case interview formulas.

Fraction and percentage shortcuts that hold

Percentages run faster through fractions than through decimals, because a fraction turns a multiplication into a division by a small integer.

Three more are worth carrying because they appear constantly: one third is 33.33 percent, one ninth is 11.11 percent, and one twentieth is 5 percent.

The use runs both ways. Forward: 12.5 percent of 4,800 is 4,800 over 8, which is 600. Backward: a share of 16.7 percent is one sixth, so the whole is six times the part. If a client holds 12.5 percent of a market and sells 300,000 units, the market is 300,000 times 8, which is 2,400,000 units. One multiplication, no division at all.

When the percentage is awkward and the base is large, find one percent and scale.

• 1 percent of 6,300 is 63. So 17 percent is 63 times 17, which is 1,071.
• 1 percent of 8,400 is 84. So 7 percent is 84 times 7, which is 588.
• 1 percent of 52,000 is 520. So 3 percent is 1,560, and 13 percent is 6,760.

Recomputed by hand. 63 times 17 is 630 plus 441, which is 1,071. 520 times 13 is 5,200 plus 1,560, which is 6,760. Choosing between the two methods takes one look: a clean fraction means divide, anything else means anchor at one percent and multiply. Ten percent is free, and from there five percent is half, twenty percent is double, and fifteen percent is ten plus five.

Refactoring a product before you multiply

Most multiplications in a case get easier after you move a factor from one side to the other. The product stays the same, and the digits get rounder.

1. 18 times 45. Halve the first and double the second: 9 times 90 is 810.
2. 24 times 35. Halve and double: 12 times 70 is 840.
3. 16 times 125. Divide by 8 and multiply by 8: 2 times 1,000 is 2,000.
4. 36 times 25. Multiplying by 25 is dividing by 4 and multiplying by 100: 3,600 over 4 is 900.
5. 3,450 divided by 5. Dividing by 5 is doubling and dividing by 10: 6,900 over 10 is 690.
6. 48 times 250. A quarter of a thousand: 48 over 4 is 12, times 1,000 is 12,000.

Recomputed by hand, each one verified against the direct product. 18 times 45 is 810. 24 times 35 is 840. 16 times 125 is 2,000. 36 times 25 is 900. 48 times 250 is 12,000.

One pattern explains all six. Multiplying one factor and dividing the other by the same number leaves the product unchanged, so you pick the pair that lands on a round number. Fives and twenty-fives want to become tens and hundreds, and even numbers want to be halved.

A companion habit saves as much time as the technique. Write both numbers down before you multiply anything. Most arithmetic errors under time are transcription errors, and a number copied wrong produces a perfectly executed wrong answer.

Keeping digits and powers of ten apart

A large number is two problems, a digits problem and an exponent problem, and solving them together is how a result comes out a thousand times too big. Work them apart.

For 4.2 million times 380:

• Digits: 4.2 times 3.8 is 15.96.
• Exponents: ten to the sixth times ten to the second is ten to the eighth.
• Combine: 15.96 times ten to the eighth is 1,596,000,000, so 1.596 billion.

Check: 4,200,000 times 380 is 1,596,000,000. The two agree. Division behaves the same way. For 7.5 million divided by 250, the digits give 7.5 over 2.5, which is 3, and the exponents give ten to the sixth over ten to the second, which is ten to the fourth. So 30,000, and 7,500,000 over 250 is indeed 30,000.

Two conventions make this reliable under time. Put every large number in the same notation before you start, so 4.2 million and 380 thousand never sit side by side in different forms. And announce the magnitude before the digits: say you expect something in the billions. That habit catches a factor of a thousand before it reaches the recommendation.

Unit conversions belong to the same discipline. McKinsey's published Electro-Light case, read through a proxy at mckinsey.com on 29 September 2026, describes a 16 ounce format as one eighth of a gallon, so a bottle count and a gallon count differ by a factor of eight.

Growth rates, doubling, and where the rule of 72 drifts

Doubling time is roughly 72 divided by the percentage growth rate, and at ordinary rates it is accurate enough to say out loud.

• At 8 percent: 72 over 8 is 9 years. Exactly, 1.08 to the ninth is 1.999, so the rule lands.
• At 5 percent over 10 years: 1.05 to the tenth is 1.62889, so about a 63 percent increase. The rule gives 14.4 years to double, which correctly implies less than double in ten.
• At 24 percent: 72 over 24 is 3 years. Exactly, 1.24 cubed is 1.9066, so the true multiple is 1.91 and the rule overstates by 4.7 percent.

Recomputed by hand, all three. The drift runs upward at high rates, so above roughly 20 percent the rule flatters the growth. Say the figure is approximate, or square it out.

The reverse direction appears more often. If revenue doubled in five years, the annual rate is 2 to the one fifth minus 1, which is 14.87 percent, and the rule of 72 gives 14.4 percent. The gap is under half a percentage point, so roughly 15 percent is defensible out loud.

One habit finishes the section. Whenever you use an approximation, announce it. Saying roughly 15 percent is a case skill. Saying 15 percent flat, when the number is 14.87, invites a challenge you did not need.

Two readings that are wrong even when the sum is right

Two failures survive a correct calculation, and both cost the point anyway.

Naming a fraction wrong. 8.6 out of 14 is 8.6 over 14, which is 0.6143, so 61.4 percent. Two thirds is 66.67 percent. The gap is 5.2 percentage points. Calling 61 percent two thirds goes past rounding into a different claim, and on a question about whether something clears a bar it flips the answer. Recomputed by hand: 14 times 0.6143 is 8.6.

Naming a rate as a ratio wrong. A threshold of 15.8 percent is not one in six. One sixth is 16.67 percent, and the inverse of 15.8 percent is 1 over 0.158, which is 6.33, so one in 6.3. The cleaner phrase overstates the threshold by almost a point.

Both errors share a cause: a plausible verbal label stuck on a number that does not quite carry it. The fix is one habit. When you turn a number into words, turn the words back into a number and check.

A unit slip does the same damage. A first-year associate at L.E.K., writing at lek.com and read on 29 September 2026, describes sizing the wedding market as though each person married separately rather than two people per wedding, and reports that the interviewer credited the method while pointing out the error. That is one person on his own experience, and the factor he names is two.

Timed case interview math exercises, with solutions

Give yourself 60 seconds per exercise, pen and paper only, and narrate each step aloud. The solutions follow immediately, so work the six first.

1. A product sells for $14.00 with a variable cost of $9.80. Volume is 1,250,000 units and fixed costs are $3,900,000. Find operating profit and operating margin.
2. Same economics. Find the break-even volume and its share of current volume.
3. Revenue grows from $320 million to $405 million over two years. Find the annual growth rate.
4. A country has 68 million people at 2.4 people per household. 35 percent of households own the appliance, it is replaced every 8 years, and it sells for $450. Size the annual replacement market.
5. Operating margin falls 1.5 points from the level in exercise 1, on the same revenue. State the fall two ways.
6. A product with a 25 percent gross margin cuts its price 8 percent. Find the volume increase that holds gross profit flat.

Solutions, all recomputed by hand on 8 October 2026.

1. Unit margin 14.00 minus 9.80 is 4.20. Contribution is 1,250,000 times 4.20, which is 5,250,000. Operating profit is 5,250,000 minus 3,900,000, so 1,350,000. Revenue is 1,250,000 times 14.00, so 17,500,000. Margin is 1,350,000 over 17,500,000, which is 7.7 percent.
2. 3,900,000 over 4.20 is 928,571 units. As a share, 928,571 over 1,250,000 is 74.3 percent, so three quarters of current volume only covers the fixed costs.
3. 405 over 320 is 1.265625, and its square root is 1.125, so 12.5 percent a year. Check: 320 times 1.125 is 360, and 360 times 1.125 is 405.
4. Households are 68,000,000 over 2.4, which is 28,333,333. 35 percent of 28,333,333 is 9,916,667 owners. Annual replacements are 9,916,667 over 8, so 1,239,583 units, and at $450 that is about $558 million.
5. 1.5 points of 17,500,000 is 262,500, so profit falls from 1,350,000 to 1,087,500. That same fall is 262,500 over 1,350,000, which is 19.4 percent of profit. A 1.5 point fall and a 19.4 percent fall are one event in two sentences, and quoting either without its base is the error.
6. Index the price at 100 with a cost of 75, so the margin is 25. After an 8 percent cut the price is 92 and the margin is 17. Holding gross profit flat needs 25 over 17, which is 1.4706, so 47.1 percent more volume.

How to practice case interview math, week by week

Six weeks splits cleanly: two weeks of isolated drills, then four weeks of whole cases. Nothing here needs an account or a purchase.

Weeks 1 and 2, twenty minutes a day, four blocks of five minutes.

1. Fraction conversion, both directions. Say the percentage from the fraction, then the fraction from the percentage. Stop yourself whenever the percentage is not actually a clean fraction.
2. Two-digit products, refactored. Twenty products, each done by moving a factor. Check three of them the long way.
3. Exponent splits. Ten large multiplications and divisions, magnitude announced before the digits.
4. The sentence after. Take yesterday's answers and write what each number means for the client, with its base and its rounding stated.

Three rules make those twenty minutes count. Time every item at 60 seconds and stop when the timer does, because an untimed drill rehearses the wrong skill. Narrate every step out loud, since a silent calculation hides exactly the chain an interviewer grades. And log each error with its type, then spend the next day's blocks on the type that recurred, which is where repetition pays.

Weeks 3 to 6, three to five full cases a week. Keep the arithmetic inside a case now. Isolated drills stop teaching once the operations are reliable, and the remaining failures are contextual: the wrong base, the dropped unit, the number with no sentence. The fourth block from weeks 1 and 2 stays in, applied to the cases.

Our math rubric weights the four things a calculation has to deliver, and the weights are ours.