Case interview mental math rewards speed, accuracy, and sensible estimation. Use these shortcuts to simplify calculations without creating unnecessary precision.
Fraction-Percentage Conversions
- 1/2: 50%
- 1/3: approximately 33.3%
- 1/4: 25%
- 1/5: 20%
- 1/6: approximately 16.7%
- 1/8: 12.5%
- 1/10: 10%
- 1/20: 5%
Percentage Shortcuts
10%: Move the decimal one place left.
5%: Calculate 10%, then divide by two.
1%: Divide by 100.
15%: Add 10% and 5%.
25%: Divide by four.
50%: Divide by two.
Multiplication Shortcuts
Multiply by 5: Multiply by 10, then divide by two.
Multiply by 25: Multiply by 100, then divide by four.
Multiply by 50: Multiply by 100, then divide by two.
Break apart numbers: 24 × 15 = (24 × 10) + (24 × 5) = 360.
Round and adjust: 49 × 20 = (50 × 20) − 20 = 980.
Powers of Ten
1 thousand: 103 = 1,000.
1 million: 106 = 1,000,000.
1 billion: 109 = 1,000,000,000.
Millions × thousands: Track zeros separately before completing the arithmetic.
Estimation Techniques
Round intelligently: Replace awkward values with nearby numbers when precision is unnecessary.
Estimate first: Predict the approximate magnitude before calculating.
Use compatible numbers: Convert figures into values that divide or multiply easily.
Preserve direction: Know whether rounding causes your estimate to be slightly high or low.
Common Case Calculation Patterns
Price × Volume: Revenue.
Revenue × Margin: Profit.
Population × Penetration: Number of customers.
Customers × Usage × Price: Market size or revenue.
Capacity × Utilization: Actual output.
Old Value × (1 + Growth Rate): New value after one period.
Accuracy Checks
- Check units: Keep thousands, millions, and billions consistent.
- Check magnitude: Make sure the answer has a sensible number of zeros.
- Reverse-check: Use the opposite operation when practical.
- Interpret: Connect the calculation to the case question.
Final principle: Mental math is not about performing complicated arithmetic instantly. Simplify the numbers, keep track of units, estimate before calculating, and prioritize a reliable answer you can explain clearly.
