Mental math practice for consulting interviews
Every case interview has math in it. Not calculus. Not statistics. Arithmetic. Percentages, multiplication, division — the kind of math you learned in middle school. The catch is that you have to do it in your head, out loud, while someone watches.
That's harder than it sounds. Most candidates know the math. Fewer can do it fast under pressure. This page covers the techniques that actually help, and gives you problems to practice with.
Why mental math matters in case interviews
Consulting firms bill clients $500-700 per hour. When a client asks "is this acquisition worth it?", the answer often comes down to a few calculations done quickly during a meeting. Consultants who need to pull out spreadsheets for basic math slow the conversation down.
In your case interview, the math tests two things: can you compute accurately without a calculator, and can you keep the conversation moving while you do it? Freezing up on "what's 15% of $240 million" is a bad signal, even if you get the answer eventually.
McKinsey, BCG, and Bain all include math-heavy cases in their interviews. Deloitte's strategy practice does the same. If you can't do the math smoothly, you won't pass.
Core techniques
Rounding and adjusting
Don't calculate 18% of $4,700. Calculate 20% of $4,700 (= $940) and subtract 2% (= $94). The answer is $846. Or round $4,700 to $5,000: 18% of $5,000 is $900, and adjust down. Close enough for a case interview.
Interviewers prefer a fast approximate answer over a slow exact one. Round aggressively, then say "roughly" before your number. They will tell you if they want more precision.
Breaking down multiplications
For 36 x 25: think of 25 as 100/4. So 36 x 100 = 3,600, divided by 4 = 900. Or break 36 into 30 + 6: (30 x 25) + (6 x 25) = 750 + 150 = 900.
Find whichever decomposition feels natural. The goal is to never hold more than two numbers in your head at once.
Percentage shortcuts
10% is just moving the decimal. 5% is half of that. 1% is moving the decimal twice. Build any percentage from these three: 17% = 10% + 5% + 2%.
For growth rates: growing at 10% per year doubles in about 7 years. Growing at 7% doubles in 10 years. This is the Rule of 72 — divide 72 by the growth rate to estimate doubling time.
Division tricks
Dividing by 5: multiply by 2 and move the decimal. (e.g. 430 / 5 = 860 / 10 = 86). Dividing by 8: divide by 2 three times. Dividing by large numbers: simplify the fraction first. $750M / $25K = 750,000,000 / 25,000 = 750,000 / 25 = 30,000.
Practice problems
Try each one in your head before checking the answer. Time yourself — aim for under 15 seconds per problem. These are the kinds of calculations that come up in actual case interviews.
A company has $340M in revenue and a 22% profit margin. What is the profit?
Show answer
$74.8M. 20% of $340M is $68M. 2% of $340M is $6.8M. Together: $74.8M.
A factory produces 1,200 units per day. Each unit sells for $45. What is daily revenue?
Show answer
$54,000. 1,200 x 45 = 1,200 x 40 + 1,200 x 5 = 48,000 + 6,000 = 54,000.
A company spent $18M on marketing and acquired 60,000 customers. What is the customer acquisition cost?
Show answer
$300. $18,000,000 / 60,000 = $18,000 / 60 = $300.
Revenue is $50M growing at 12% per year. What will it be in 3 years?
Show answer
Roughly $70M. Year 1: $56M. Year 2: $62.7M. Year 3: $70.2M. Shortcut: 12% for 3 years is about 40% total (slightly more due to compounding), so $50M x 1.4 = $70M.
A city has 2 million people. 40% are between 25-55. 30% of that group goes to a gym. Average gym membership is $50/month. What is the monthly gym market?
Show answer
$12M/month. 2M x 0.4 = 800K. 800K x 0.3 = 240K gym members. 240K x $50 = $12M.
Costs dropped from $85M to $72M. What is the percentage decrease?
Show answer
About 15.3%. Decrease is $13M. $13M / $85M. 10% of $85M is $8.5M. 15% is $12.75M. So it is just over 15%.
$2.4B in revenue, 80,000 employees. What is revenue per employee?
Show answer
$30,000. $2,400,000,000 / 80,000 = $2,400,000 / 80 = $30,000.
A store has 350 locations averaging $1.8M in annual revenue each. Total revenue?
Show answer
$630M. 350 x $1.8M = 350 x 2M - 350 x 0.2M = $700M - $70M = $630M.
Fixed costs are $500K/year. Variable cost per unit is $8. Selling price is $20. How many units to break even?
Show answer
About 41,667 units. Contribution per unit = $20 - $8 = $12. $500,000 / $12 = 41,667.
The US has 130 million households. 65% own a car. Average household spends $200/month on gas. What is the annual US consumer gasoline market?
Show answer
Roughly $203B. 130M x 0.65 = 84.5M car-owning households. 84.5M x $200 x 12 = 84.5M x $2,400 = ~$203B.
How to get faster
Practice every day, not every weekend
15 minutes a day beats a 2-hour weekend session. Mental math is muscle memory. You build it with daily repetition, not occasional cramming.
Say your work out loud
In the interview, you'll talk through your math. Practice that now. Saying "so 15% of 800 is 120" out loud while solving forces your brain to process differently than silent calculation.
Time yourself
Without time pressure, practice is just homework. Set a 10-second target per problem and work toward it. CaseXcel's drill mode does this automatically.
Work on your weaknesses
If you are slow at division, do more division. Practicing what you're already good at feels productive but doesn't make you better. Find what trips you up and drill that.
Frequently asked questions
How fast should I be at mental math for consulting interviews?
You should handle two-digit multiplication, percentage calculations, and basic division within 10-15 seconds. Interviewers expect you to compute without reaching for a calculator.
What types of math come up in case interviews?
Percentages (growth rates, margins, market share), multiplication (revenue calculations), division (per-unit costs), and estimation (market sizing). You rarely need anything beyond arithmetic, but you need to do it fast and without mistakes.
How long does it take to get good at consulting mental math?
Most people see real improvement after 2-3 weeks of daily practice, around 15 minutes per day. Speed comes from pattern recognition, and that comes from repetition.
Practice mental math on your phone
These problems are a starting point. CaseXcel gives you hundreds more, with adaptive difficulty that adjusts to your skill level. You get timed drills, speed tracking, and daily practice reminders.
If you're preparing for a consulting interview, 15 minutes a day on CaseXcel will make a measurable difference in your math speed within two weeks.