Case interview maths: the calculations and shortcuts you need

Case maths is not hard maths. It is arithmetic done by hand, under observation, with large numbers. Interviewers watch for accuracy, a clear method and what you conclude from the result.

What comes up

• Percentages and percentage change.
• Margins: profit / revenue.
• Break-even: fixed costs / contribution per unit.
• Growth: compound growth over a few years.
• Market share and market size.
• Payback and simple returns.
• Weighted averages.

Shortcuts

Use round numbers and adjust. 19% of 420: take 20% (84) and subtract 1% (4.2) to get about 80.

Split percentages. 35% = 25% + 10%. 17.5% = 10% + 5% + 2.5%.

Handle zeros separately. 3.2 million × 450: 3.2 × 450 = 1,440, then add six zeros: 1.44 billion.

Rule of 72. Years to double ≈ 72 / growth rate. At 6% growth, about 12 years.

Fractions. 1/6 ≈ 16.7%, 1/7 ≈ 14.3%, 1/8 = 12.5%, 1/9 ≈ 11.1%.

Growth over two or three years. 10% for three years ≈ 33%, not 30%.

Talk it through

1. Say the approach before calculating. "I will find contribution per unit, then divide fixed costs by it."
2. Write neatly in a table.
3. Say intermediate results aloud so the interviewer can follow and correct a slip.
4. Sense-check the answer against something you know.
5. Say what it means. "Break-even is 40,000 units, which is 80% of capacity, so there is little room for error."

Worked example

A factory has fixed costs of €2.4m. Each unit sells for €50 and costs €30 to make. Capacity is 150,000 units.

• Contribution = €20 a unit.
• Break-even = 2.4m / 20 = 120,000 units.
• That is 80% of capacity. "The plant must run nearly full to make money. I would look at price and variable cost next."

If you make a mistake

Say so, correct it and move on. A calm correction is a point in your favour.

Daily practice

Ten minutes a day for two weeks: percentages, large-number multiplication and division, and one break-even. The free consulting sampler has timed drills.