Case interview math is usually straightforward. The challenge is setting up the calculation correctly, working efficiently, and interpreting what the answer means for the client.
Percentages and Fractions
Percentage: Part ÷ Whole × 100.
Percentage change: (New Value − Old Value) ÷ Old Value × 100.
Percentage points: The absolute difference between two percentages. Moving from 20% to 25% is a 5-percentage-point increase.
Useful conversions: 1/2 = 50%, 1/3 ≈ 33%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, and 1/10 = 10%.
Growth and CAGR
Growth rate: (New Value ÷ Old Value) − 1.
CAGR: (Ending Value ÷ Beginning Value)1/n − 1, where n is the number of years.
Rule of 72: Divide 72 by the annual growth rate to estimate how many years it takes a quantity to double.
Revenue, Profit, and Margins
Revenue: Price × Volume.
Profit: Revenue − Costs.
Profit margin: Profit ÷ Revenue.
Contribution margin per unit: Price − Variable Cost per Unit.
Market share: Company Sales ÷ Total Market Sales.
Breakeven and Economics
Breakeven volume: Fixed Costs ÷ Contribution Margin per Unit.
ROI: Gain or Profit from Investment ÷ Investment Cost.
Payback period: Initial Investment ÷ Annual Cash Benefit when annual benefits are relatively constant.
Weighted Averages
Weighted average: Multiply each value by its corresponding weight, add the results, and divide by the total weight if the weights do not already sum to 100%.
Use weighted averages when customer segments, products, prices, or probabilities contribute differently to an overall result.
Capacity and Operations
Utilization: Actual Output ÷ Maximum Capacity.
Productivity: Output ÷ Input.
Yield: Good Output ÷ Total Input.
Throughput: Units processed during a specified period.
Expected Value and Probability
Expected value: Sum of each possible outcome multiplied by its probability.
Probability: Favorable Outcomes ÷ Total Possible Outcomes, when outcomes are equally likely.
Case Math Best Practices
- Write the equation first: Explain what you are calculating before doing arithmetic.
- Track units: Clearly distinguish dollars, units, percentages, millions, and billions.
- Estimate first: Know the approximate answer before calculating precisely.
- Sanity-check: Ask whether the result is realistic.
- Interpret: Always explain what the number means for the client.
Final principle: Case math is not primarily a test of difficult mathematics. Strong candidates combine accurate calculations with clear setup, sensible assumptions, efficient arithmetic, and business interpretation.
