Author: Taylor Warfield, Former Bain Manager and interviewer

Last Updated: July 13, 2026

 

Case interview math practice problems are the fastest way to build the speed and accuracy you need to pass quantitative case questions at McKinsey, BCG, and Bain. This guide gives you 35 realistic drills with full worked solutions, the formulas behind them, and a daily routine that gets you interview-ready in two to three weeks.

 

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Key Takeaways

 

The best way to prepare for case interview math is to drill realistic problems across percentages, growth, breakeven, market sizing, and returns until you can solve each type quickly and explain what the answer means for the business.

 

• Roughly 90% of case math uses five skills: multiplication, division, percentages, fractions, and basic algebra

 

• You get no calculator, so every calculation is done mentally or on paper

 

• State the formula, walk through your approach, calculate, then explain the "so what" for the client

 

• McKinsey expects precise figures while BCG and Bain allow more rounding

 

• Drill 15 to 20 minutes a day for two to three weeks and target 95% accuracy

 

• Practice each problem inside a business context, not as abstract arithmetic

 

What Are Case Interview Math Practice Problems?

 

Case interview math practice problems are short quantitative exercises that mirror the calculations consultants run inside a case, such as margins, breakeven volume, growth rates, market sizing, and returns on investment. You solve them without a calculator, state your formula and approach out loud, compute the answer, then explain what it means for the client.

 

The math itself is the arithmetic you learned by age 13. What makes it hard is doing it fast, doing it flawlessly, and connecting the result back to a business decision while an interviewer watches.

 

That last part is what separates strong candidates from weak ones. A number with no interpretation is worth almost nothing in a case. The drills below train both halves: the calculation and the meaning behind it. For the full theory and shortcuts, work through these problems alongside our guide to case interview math.

 

Why Do Consulting Firms Test Math in Case Interviews?

 

Consulting firms test math because consultants use quantitative analysis every day to size opportunities, pressure-test ideas, and decide where to dig. According to McKinsey's careers page, the problem-solving interview is designed to evaluate your analytical thinking and approach to complex problems, and quick numerical reasoning sits at the center of that.

 

There are three reasons math earns so much weight in the evaluation.

 

It proves you can prioritize. A fast estimate tells the team whether an idea is worth more analysis or should be dropped. That judgment is the core of consulting work.

 

It shows you stay calm under pressure. Doing accurate math while talking out loud is uncomfortable. Interviewers want to see you keep a clear head when the stakes are high.

 

It reveals business sense. The interpretation matters as much as the answer. A candidate who calculates a number and then explains the implication for the client is thinking like a consultant.

 

In my experience interviewing at Bain, the candidates who froze on math rarely recovered, even with a brilliant structure. Numbers are the part of the case you can fully control with preparation, so there is no excuse to lose points here.

 

What Formulas Do You Need for Case Interview Math?

 

You need a small set of business formulas, not advanced finance. The table below covers the ones that appear in the vast majority of cases, and you should be able to recall and apply each from memory.

 

Concept	Formula
Profit	Revenue minus total costs
Gross margin	(Revenue minus COGS) divided by revenue
Profit margin	Profit divided by revenue
Percent change	(New value minus old value) divided by old value
Contribution margin	Price minus variable cost per unit
Breakeven volume	Fixed costs divided by contribution margin per unit
Market share	Company revenue divided by total market revenue
ROI	Net profit divided by investment cost
Payback period	Investment cost divided by annual cash flow
Rule of 72	72 divided by the growth rate equals years to double

 

Memorize these cold so you never burn interview time recalling them. If you want a one-page reference to keep beside you while you drill, our consulting math cheat sheet lays them all out.

 

You can also study the full set of case interview formulas with worked derivations to see how each one comes together.

 

How Should You Solve Every Case Math Problem?

 

Use the same four steps on every problem so your process becomes automatic. This structure keeps you accurate, keeps the interviewer with you, and turns a raw number into a recommendation.

 

1. State the formula: say what you are solving for and which formula gets you there before you touch a number
   
   
2. Walk through your approach: lay out the steps out loud so the interviewer can follow and catch any wrong turn early
   
   
3. Calculate in chunks: break the arithmetic into small pieces, keep units on every line, and track your zeros carefully
   
   
4. Give the "so what": explain what the answer means for the client and what you would look at next

 

The biggest quant error in cases is mixing millions and billions because units got dropped. Writing the unit next to every figure prevents it. The second biggest is rushing the setup, so slow down for two seconds before you start multiplying.

 

Case Interview Math Practice Problems With Solutions

 

Below are 35 problems grouped by type and ordered from quick warm-ups to multi-step questions. Cover the solution, solve on paper with a timer, then check yourself. Every number here is a round, illustrative figure chosen to teach the method, not a real company statistic.

 

Percentages and Margins (Problems 1 to 8)

 

Percentages are the foundation of every case. You will use them for margins, growth, market share, and cost breakdowns, so if you drill one category hardest, make it this one.

 

Problem 1: A product sells for $80 and costs $50 to make. What is the gross margin?

Solution: Gross profit is $80 minus $50, which is $30. Divide $30 by the $80 price to get a gross margin of 37.5%.

 

Problem 2: A company has $500M in revenue and $75M in net income. What is the net profit margin?

Solution: Divide $75M by $500M to get 15%. For every dollar of sales, the company keeps 15 cents in profit.

 

Problem 3: A client's revenue rises from $40M to $50M. What is the percentage increase?

Solution: The change is $10M. Divide $10M by the original $40M to get a 25% increase.

 

Problem 4: A market is worth $2.5B. The client holds 18% of it. What is the client's revenue?

Solution: Split 18% into 10% plus 8%. Ten percent of $2.5B is $250M and 8% is $200M, so the client's revenue is $450M.

 

Problem 5: A store has $1.5M in revenue and $1.2M in costs. What is the operating margin?

Solution: Operating profit is $1.5M minus $1.2M, or $0.3M. Divide $0.3M by $1.5M to get a 20% operating margin.

 

Problem 6: A subscription product has 2M users and loses 6% of them each month. How many users churn in a month?

Solution: Take 6% of 2M users. That is 120,000 users lost per month.

 

Problem 7: A product's price rises from $25 to $30. What is the percentage increase?

Solution: The change is $5. Divide $5 by the original $25 to get a 20% increase.

 

Problem 8: A factory runs at 80% of its 5,000-unit daily capacity. How many units does it make per day?

Solution: Take 80% of 5,000 units. The factory produces 4,000 units per day.

 

Growth Rates and CAGR (Problems 9 to 13)

 

Growth questions show up in almost every growth strategy case. The trick is to estimate compound growth fast rather than computing exact exponents.

 

Problem 9: Revenue starts at $100M and grows 10% per year for three years. Estimate the ending revenue.

Solution: A quick estimate adds the growth rates: 30% on $100M gives roughly $130M. The exact figure is $100M times 1.1 cubed, or about $133M, so the shortcut lands within a few percent.

 

Problem 10: A metric grows 8% per year. How many years until it doubles?

Solution: Use the Rule of 72. Divide 72 by 8 to get 9 years to double.

 

Problem 11: A market doubles in 6 years. What is the approximate annual growth rate?

Solution: Rearrange the Rule of 72. Divide 72 by 6 years to get roughly 12% growth per year.

 

Problem 12: Price rises 20% and volume falls 10%. What is the net effect on revenue?

Solution: Multiply the growth factors: 1.20 times 0.90 equals 1.08. Revenue rises by about 8%.

 

Problem 13: Revenue grows from $200M to $242M over two years. What is the approximate annual growth rate?

Solution: Total growth is $42M on $200M, or 21% over two years. The square root of 1.21 is 1.1, so the compound annual growth rate is about 10%.

 

Breakeven and Pricing (Problems 14 to 19)

 

Breakeven and pricing math separates prepared candidates from unprepared ones because it pairs a formula with business logic. Nearly every pricing case and new product case asks some version of these questions.

 

Problem 14: Fixed costs are $2M, the price is $50, and the variable cost is $30 per unit. What is the breakeven volume?

Solution: Contribution margin is $50 minus $30, or $20 per unit. Divide $2M in fixed costs by $20 to get a breakeven of 100,000 units.

 

Problem 15: Using Problem 14, the total market is 1M units per year. What share must the client win just to break even?

Solution: Divide the 100,000 breakeven units by the 1M unit market. The client needs a 10% share to break even, which is a useful reality check on whether the launch is realistic.

 

Problem 16: A product is priced at $200 with a variable cost of $120. What is the contribution margin per unit and as a percentage?

Solution: Contribution margin is $200 minus $120, or $80 per unit. As a percentage that is $80 divided by $200, which is 40%.

 

Problem 17: Fixed costs are $600K and the contribution margin is 40% on a $200 price. What is the breakeven in revenue and units?

Solution: Breakeven revenue is $600K divided by 0.40, which is $1.5M. At $200 per unit, that is 7,500 units.

 

Problem 18: A client wants $1M in profit. Fixed costs are $2M and contribution margin is $20 per unit. How many units must it sell?

Solution: Add the $2M fixed costs and the $1M profit target to get $3M. Divide $3M by the $20 contribution margin to get 150,000 units.

 

Problem 19: A price cut takes a product from $50 to $45, with a $30 variable cost. By how much must volume rise to keep total contribution flat?

Solution: The old contribution margin was $20 and the new one is $15. To hold contribution constant, divide $20 by $15, so volume must rise about 33%.

 

Case interviews are heavy on math like this, and speed comes from doing the same problem types over and over. If you want to learn case math quickly, my case interview course walks you through every calculation type with timed drills.

 

Market Sizing (Problems 20 to 24)

 

Market sizing tests whether you can build a sensible estimate from a few assumptions. The math is simple multiplication, so the skill is structuring the chain and sanity-checking the result, which you can drill further with dedicated market sizing practice.

 

Problem 20: Estimate the annual coffee market in a country of 300M people, where half drink coffee, each averages 2 cups a day, and a cup costs $2.

Solution: Half of 300M is 150M drinkers, each buying 2 cups for 350 days, or about 700 cups a year. That is 105B cups at $2 each, or roughly $210B per year.

 

Problem 21: Estimate the number of gas stations in a city of 1M people.

Solution: Assume 500,000 cars, each filling up once a week, for 500,000 fill-ups a week. A station handling about 500 cars a day serves roughly 3,500 a week, so the city needs around 140 stations.

 

Problem 22: Estimate the annual market for replacement tires where there are 250M cars, each with 4 tires replaced every 5 years, at $100 per tire.

Solution: Total tires in use are 250M times 4, or 1B, and one fifth are replaced yearly, giving 200M tires. At $100 each, the market is about $20B per year.

 

Problem 23: Estimate the annual diaper market where there are 4M births a year, babies wear diapers for 2.5 years, and use 6 a day.

Solution: Babies in diapers at any time are roughly 4M times 2.5, or 10M. At 6 diapers a day for 365 days, that is about 22B diapers, and at $0.25 each the market is roughly $5.5B.

 

Problem 24: Estimate the number of piano tuners needed in a city of 1M people, where there is 1 piano per 100 people, tuned once a year.

Solution: That is 10,000 pianos and 10,000 tunings a year. A tuner doing 4 a day for 250 days handles 1,000 a year, so the city needs about 10 tuners.

 

ROI, Payback, and NPV (Problems 25 to 29)

 

Investment math comes up whenever a client weighs spending money today against returns later. You do not need exact present-value tables, but you should handle ROI, payback, and a rough net present value in your head.

 

Problem 25: An investment of $50,000 generates $10,000 in profit a year. What is the payback period?

Solution: Divide the $50,000 cost by the $10,000 annual return. The payback period is 5 years.

 

Problem 26: An investment of $80,000 returns a net profit of $20,000. What is the ROI?

Solution: Divide $20,000 by $80,000 to get 25%. That single-year return helps compare this option against alternatives.

 

Problem 27: A client invests $60M and earns $15M in added profit each year. What is the payback period?

Solution: Divide $60M by $15M. The investment pays back in 4 years, which is attractive for most strategic projects.

 

Problem 28: An investment of $100,000 returns $30,000 a year for 5 years at a 10% discount rate. Is the NPV positive?

Solution: The five-year annuity factor at 10% is about 3.8, so the present value of the cash flows is roughly $30,000 times 3.8, or $114,000. Subtract the $100,000 cost and the NPV is about positive $14,000, so the client should invest.

 

Problem 29: Project A returns $1.5M on $5M invested. Project B returns $1.2M on $3M. Which is more capital-efficient?

Solution: Project A has a 30% return and Project B has a 40% return. Project B is more efficient per dollar, though A delivers more total profit, so the right choice depends on whether capital is the constraint.

 

Market Share and Multi-Step Profitability (Problems 30 to 35)

 

These problems chain two or three steps together, which is how math usually appears inside a real case. Slow down on the setup, because a profitability question rewards a clean structure more than raw speed.

 

Problem 30: A client has $300M in revenue inside a $1.5B market. What is its market share?

Solution: Divide $300M by $1.5B. The client holds a 20% market share.

 

Problem 31: A market is worth $4B and the top 4 players hold 20% combined. If they are roughly equal, what is each one's revenue?

Solution: The top 4 together earn 20% of $4B, or $800M. Split evenly, each holds about $200M.

 

Problem 32: Revenue falls 5% from $200M while costs stay flat at $160M. What happens to profit?

Solution: New revenue is $190M against $160M in costs, so profit drops from $40M to $30M. That is a 25% decline in profit from a 5% revenue dip, which shows how a small revenue change magnifies into a large profit swing.

 

Problem 33: A client with $500M in revenue and $450M in costs wants to lift profit from $50M to $55M by cutting cost. How much must costs fall?

Solution: To reach $55M in profit on $500M in revenue, costs must drop to $445M. That is a $5M cut, or about 1.1% of current costs.

 

Problem 34: A company sells 10M units at $10 each, with a $6 variable cost and $30M in fixed costs. What is its profit?

Solution: Contribution is 10M units times $4, or $40M. Subtract the $30M in fixed costs to get $10M in profit.

 

Problem 35: Using Problem 34, the client raises price 10% to $11 and loses 5% of volume, falling to 9.5M units. What is the new profit?

Solution: New contribution is 9.5M units times $5, or $47.5M, and after the $30M in fixed costs, profit is $17.5M. Profit jumps from $10M to $17.5M, so the price increase is highly accretive even with the volume loss.

 

What Are the Most Common Case Math Mistakes?

 

Most lost points in case math come from a handful of avoidable errors, not from hard arithmetic. Watch for these as you drill so you stop making them before the interview.

 

• Dropping units and mixing millions with billions, which is the single most common error

 

• Diving into calculation before stating the formula and approach, so the interviewer cannot follow you

 

• Rushing the setup and answering a slightly different question than the one asked

 

• Stopping at the number and forgetting the "so what" that ties it back to the client

 

• Rounding too aggressively in a McKinsey case where precise figures are expected

 

Cleaning up your zeros and your handwriting fixes more of these than any speed trick. Circle each answer and keep your scratch work in neat columns so you can retrace any step. To push your raw speed higher, work through targeted case interview mental math shortcuts until they feel automatic.

 

How Should You Practice Case Interview Math?

 

Practice in two phases: first build raw calculation speed, then move the same math inside full cases. Consistency beats marathon sessions, so a short daily routine works better than one long weekend cram.

 

If your basic arithmetic feels rusty, spend a few days on a free arithmetic refresher before you start timing case problems. Solid fundamentals make every drill below more productive.

 

Here is a 15-minute daily routine that works for most candidates.

 

1. Minutes 1 to 5: percentages and margins, targeting under 10 seconds per calculation
   
   
2. Minutes 6 to 10: one breakeven or pricing problem, targeting under 30 seconds including the business interpretation
   
   
3. Minutes 11 to 15: one market sizing chain plus a one-sentence statement of what the number means

 

Track your times across days and you should see clear improvement within a week. Run rapid-fire reps with case interview math drills to keep your speed sharp between sessions.

 

Once your raw speed is solid, the more valuable practice is solving math inside a complete case, where you also have to set up the problem and interpret the result. Work through full case interview examples so the math stops feeling separate from the case.

 

The fastest feedback loop is a coach who has actually given these interviews and can spot the small errors a peer would miss. If you want targeted feedback on your math and your case performance, my case interview coaching pairs you with a former Bain interviewer.

 

Working through case interview math practice problems every day is the surest way to remove the one variable you can fully control, so start your timed drills today and keep them up until interview week.

 

Frequently Asked Questions

 

How hard is case interview math?

 

Case interview math is not hard in terms of the math itself. It uses middle-school arithmetic such as multiplication, division, percentages, and fractions. The difficulty comes from doing it quickly and accurately under pressure without a calculator, and from interpreting what the number means for the business.

 

Can you use a calculator in a case interview?

 

No. Calculators are not allowed in consulting case interviews, whether in person or virtual. You are expected to do all calculations mentally or on paper, which is why mental math practice matters so much during preparation.

 

How long does it take to prepare for case interview math?

 

Most candidates reach the required speed and accuracy in two to three weeks of focused practice. Plan for 15 to 20 minutes of timed math drills per day, plus extra math reps inside full practice cases. Candidates who start far below target may need four weeks.

 

What math do you need for a case interview?

 

You need fast, accurate arithmetic plus a handful of business formulas. The core skills are multiplication, division, percentages, fractions, and basic algebra. The core formulas are margins, growth rates, breakeven volume, market sizing logic, and simple returns such as ROI and payback period.

 

Is case interview math different at McKinsey, BCG, and Bain?

 

The underlying math is the same, but expectations differ slightly. McKinsey tends to expect more precise calculations in its interviewer-led format. BCG and Bain generally allow more rounding and estimation in candidate-led cases, though you should practice without rounding so you can choose to round only when it is safe.

 

How do I practice case interview math by myself?

 

Drill timed problems by category, starting with percentages and margins, then moving to breakeven, growth, market sizing, and returns. Write the formula first, keep units on every line, and say the business meaning out loud after each answer. Once your raw speed is solid, practice the same math inside full cases.

 

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