Mental Math for Consulting: 12 Shortcuts You Can't Afford to Miss
Most candidates lose math points not because the arithmetic is hard, but because they are doing it the slow way. Twelve shortcuts that compound across an hour of casing.
The math content of a case is rarely above 8th-grade algebra. What makes it hard is doing it under pressure, talking out loud, while an interviewer is watching for whether you flinch. The good news is that almost every "fast math" candidate is using the same dozen shortcuts — and you can learn them in an evening.
1. Round, do, correct
Almost no case math benefits from carrying three decimals through the calculation. Round to clean numbers, do the math, then either explicitly correct at the end or note the rounding direction. "About $480M, slightly low because I rounded the customer count down" is more impressive than a precise number computed slowly.
2. Convert percentages to fractions
25% is one-quarter. 33% is one-third. 12.5% is one-eighth. 16.7% is one-sixth. 40% is two-fifths. Whenever you see one of these, switch to the fraction; it almost always cancels something.
3. Multiply by 11 trick
For a two-digit number times 11: add the digits and put the sum in the middle. 36 × 11 = 3_(3+6)_6 = 396. Comes up more often than you would expect once you start watching for it.
4. Squaring numbers ending in 5
For X5²: take X, multiply by X+1, append 25. So 35² = 3 × 4 = 12, append 25 → 1,225. 75² = 7 × 8 = 56, append 25 → 5,625.
5. Growth rate compounding rule of 72
Years to double = 72 / growth rate. 8% grows for 9 years to double. 6% takes 12 years. Use it constantly when interviewers give you a CAGR and ask about a multi-year horizon.
6. Percentage change as multiplication
Up 20% then down 20% is not flat — it is 0.96. Always convert percentage changes to multipliers (1.2 × 0.8) and remember directionally that compounding two opposite percentage changes leaves you slightly below the starting point.
7. Big numbers as scientific notation
Stop counting zeros out loud. 3.2 billion × 4% = 3.2 × 10⁹ × 4 × 10⁻² = 12.8 × 10⁷ = $128M. Practice this until it is automatic. It eliminates an entire category of "wait, was that millions or billions" errors.
8. Anchor calculations to %s of revenue
Most case math involves percentages of a top-line number you already wrote down. Rather than re-deriving each line, scale to revenue. "If revenue is $1B and contribution margin is 40%, that is $400M. R&D at 8% is $80M…" Each line takes 3 seconds.
As you do these calculations, narrate the structure, not the arithmetic. "I am taking 8% of $1B, so $80M." Not "1, 0, 0, carry the…" The interviewer is grading your reasoning, not your scratch work.
9. Divide by clean numbers
Dividing by 25? Multiply by 4 and divide by 100. Dividing by 50? Multiply by 2 and divide by 100. Dividing by 7.5? Multiply by 4, divide by 30 (or 3, then 10).
10. Double-and-halve
16 × 25 → 8 × 50 → 4 × 100 = 400. Whenever one factor is even and the other is messy, doubling-and-halving collapses the math.
11. Sanity-check by order of magnitude
Before you state the answer, ask: should this be in the thousands, millions, or billions? If the US auto market is 17M new vehicles a year, an answer of "230 cars" or "230 trillion cars" is wrong regardless of your arithmetic. Order-of-magnitude check catches 90% of fatal errors.
12. Recover loudly when wrong
Everyone makes mistakes under pressure. The candidates who lose offers are not the ones who made an error — they are the ones who tried to hide it. "I want to redo that — I think I dropped a zero" is a clean recovery. Quietly correcting the answer two steps later is not.
Drilling these
The point of these shortcuts is to free your working memory for the structural reasoning. None of them help if you have to think about which one to use. Spend 15 minutes a day for two weeks running anki-style drills on each. After that, you will not be consciously choosing — you will just be faster.
Market Sizing: From Top-Down to Bottom-Up in 90 Seconds
The math companion piece — how to land a defensible market size under pressure without burning the case clock.
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