Fast mental math is a superpower in consulting interviews. You don’t need to be a math genius—but you do need to work quickly, accurately, and out loud.
This article covers the most useful shortcuts for percentage calculations, working with multiples, and estimating compound annual growth rate (CAGR). Master these, and you’ll speed up every case you face.
1. Percentages: The Art of “Friendly Numbers”
Percentage problems show up constantly—revenue drops, margin changes, growth rates. Rather than memorizing formulas, get used to quick breakdowns:
“Revenue increased from $100M to $115M → that’s a 15% increase.”
Common tricks:
- 10% of any number: Just move the decimal. 10% of 450 = 45
- 5% = 10% ÷ 2: 5% of 450 = 22.5
- 1% = 10% ÷ 10: 1% of 450 = 4.5
- % Change = (New – Old) / Old × 100
2. Gross Margin & Contribution Margin
Consultants often estimate margins mentally. A useful trick is using friendly benchmarks:
“Selling price is $80, cost is $60 → margin = 25% ($20/$80)”
But note that some firms use contribution margin over price, while others use it over cost or revenue. Always clarify.
3. Multiples: Reverse Engineering Numbers
Valuation and investment cases often mention multiples like “P/E ratio” or “EBITDA multiple.” Here’s how to use them fast:
“If the EBITDA is $10M and the multiple is 8x, then valuation ≈ $80M.”
In reverse:
- Valuation ÷ Multiple = Earnings or EBITDA
- Revenue × Margin = Profit (→ used in many multiples)
When comparing companies, think: higher multiple = higher growth or quality expectations.
4. CAGR: Estimate Long-Term Growth
CAGR helps you estimate average annual growth over multiple years. The formula is:
CAGR = [(Final / Initial) ^ (1/n)] – 1
But in an interview, there’s no time for a calculator. Try these approximations instead:
- Rule of 72: 72 ÷ CAGR% ≈ doubling time in years
- Shortcuts for 2–3 year periods:
“Revenue grew from $100M to $121M in 2 years → CAGR is ~10% (since 1.1² = 1.21)”
“Grew from $100M to $133M in 3 years → CAGR ≈ 10% (1.1³ = 1.33)”
5. Estimating with Ranges and Benchmarks
When math gets messy, use round numbers and give a range:
“The market is likely between $450M and $550M depending on usage assumptions.”
Use mental benchmarks:
- 1/3 ≈ 33%, 1/4 = 25%, 1/5 = 20%, 1/10 = 10%
- 2× = 100% growth, 3× = 200% growth
- √10 ≈ 3.16 → useful for growth intuition
6. Practice: Can You Solve These Fast?
- Question: A product sells for $80 and costs $60. What’s the margin?
- Question: A company’s revenue grew from $200M to $300M in 3 years. Estimate the CAGR.
- Question: A company’s P/E ratio is 20 and profit is $5M. What’s the valuation?
Try solving in under 30 seconds each. Say your logic out loud.
Final Thoughts
Math speed isn’t about being perfect—it’s about being confident, quick, and structured. With a handful of shortcuts and daily practice, you’ll turn mental math from a stress point into a strength.
Fast math = faster thinking = better performance in case interviews.