Author: Taylor Warfield, Former Bain Manager and interviewer

Last Updated: May 19, 2026

 

Case interview math drills are timed practice problems that build the speed and accuracy you need to pass quantitative questions at McKinsey, BCG, Bain, and other top consulting firms. The math itself is middle school level. The challenge is doing it fast, under pressure, with no calculator.

 

By the end of this article, you will have 30+ worked drill problems across the five core math categories, a daily practice routine, and the exact mistakes to avoid as you train.

 

But first, a quick heads up:

 

McKinsey, BCG, Bain, and other top firms accept less than 1% of applicants every year. If you want to triple your chances of landing interviews and 8x your chances of passing them, watch my free 40-minute training.

 

What Are Case Interview Math Drills?

 

Case interview math drills are short, timed practice problems designed to build speed and accuracy on the arithmetic you will face in consulting interviews. Each drill focuses on one math skill at a time, such as percentages, growth rates, or breakeven analysis. The goal is to make these calculations automatic.

 

When you are sitting across from a McKinsey partner and need to compute 15% of 320 million, you should not have to stop and think. Drilling these problems daily for 2 to 3 weeks builds that automaticity. Most candidates who pass MBB interviews have done 500 to 1,000 drill problems before their first live interview.

 

Drills are different from full case practice. In a full case, you must structure a problem, ask clarifying questions, do math, and interpret results all at once. Drills isolate the math piece so you can build speed without juggling everything else.

 

Why Do Case Interview Math Drills Matter?

 

Case interview math drills matter because the math itself is simple, but speed and accuracy under pressure separate offers from rejections. According to MBB recruiting data, weak quantitative performance is one of the top three reasons candidates fail second-round interviews. Drills build the muscle memory you need to stay calm and accurate when an interviewer is watching every keystroke on your scratch paper.

 

There are four reasons math drills are non-negotiable for case interview prep:

 

• They build raw calculation speed. Most candidates can solve case math given unlimited time, but interviews are timed. Drills get your solving time per problem under 60 seconds.

 

• They build accuracy. Based on McKinsey's recruiting materials, even small errors during a case can derail your entire recommendation. Drills train you to spot magnitude mistakes before they happen.

 

• They build confidence. The biggest reason candidates freeze on math is fear. When you have done 500 percentage problems, no percentage problem can rattle you.

 

• They isolate weaknesses. Many candidates think they are bad at math when really they are slow at one specific operation. Drills surface the exact gap so you can fix it.

 

In my experience coaching hundreds of candidates at Bain and through my course, the ones who drill daily for 2 to 3 weeks before interviews dramatically outperform those who only practice math inside full cases.

 

What Are the 5 Categories of Case Interview Math Drills?

 

There are five core categories of case interview math drills you should master:

 

• Percentage drills

 

• Multiplication and division drills

 

• Growth rate and CAGR drills

 

• Breakeven and profitability drills

 

• Market sizing drills

 

These five categories cover more than 95% of the math you will see in real interviews at McKinsey, BCG, Bain, Deloitte, and other top firms. Each section below gives you a small set of drills with full worked solutions so you can practice immediately.

 

Drill Category	Interview Frequency	Difficulty	Target Time
Percentages	Very high	Easy to medium	20 to 45 seconds
Multiplication and division	Very high	Easy to medium	30 to 60 seconds
Growth and CAGR	High	Medium	45 to 60 seconds
Breakeven and profitability	High	Medium	60 to 90 seconds
Market sizing	Medium	Medium to hard	3 to 5 minutes

 

How Should You Drill Percentages for Case Interviews?

 

Drill percentages first and most often because they appear in every case interview. Percentages show up in margin calculations, growth rates, market share questions, and cost breakdowns. If you only drill one category, drill this one. Aim for 30 to 40% of your daily math practice on percentages.

 

Use the 10% and 1% anchor trick for almost every percentage problem. To find 23% of 480, calculate 10% (48), double it to get 20% (96), then add 3% (14.4) to reach 110.4. This approach is faster and more accurate than long multiplication and is what top consultants use in real client meetings.

 

Percentage Drill Problems with Solutions

 

Problem 1: What is 15% of 320?

 

Solution: 10% of 320 is 32. 5% is half of that, or 16. 15% equals 32 plus 16, which is 48.

 

Problem 2: What is 35% of 240?

 

Solution: 10% of 240 is 24. 30% is 72. 5% is 12. 35% equals 72 plus 12, which is 84.

 

Problem 3: A company's revenue grew from $80 million to $100 million. What is the growth rate?

 

Solution: Growth is $20 million on a base of $80 million. 20 divided by 80 equals 0.25, or 25%.

 

Problem 4: A product costs $45 to produce and sells for $75. What is the gross margin?

 

Solution: Gross profit is $30 on revenue of $75. 30 divided by 75 equals 0.40, or 40%.

 

Problem 5: A market is $2 billion and your client holds 12% market share. What is your client's revenue?

 

Solution: 10% of $2 billion is $200 million. 1% is $20 million. 12% equals $200 million plus $40 million, or $240 million.

 

Problem 6: If costs are $80 million and revenues are $120 million, what is the profit margin?

 

Solution: Profit is $40 million on revenue of $120 million. 40 divided by 120 equals 0.33, or 33%.

 

Aim to solve each percentage drill in under 30 seconds. If you are over 45 seconds, slow down and review the anchor method until it becomes automatic.

 

How Should You Drill Multiplication and Division?

 

Drill multiplication and division using the distributive property to break large numbers into smaller, manageable pieces. These drills test the large-number arithmetic that appears in market sizing, revenue calculations, and cost analysis. Trying to multiply 4-digit numbers in one step is where most candidates make errors.

 

For 230 times 45, break it into (200 times 45) plus (30 times 45) which equals 9,000 plus 1,350 or 10,350. For division, cancel zeros first and reduce by common factors before computing. Both techniques cut calculation time in half.

 

Multiplication and Division Drill Problems with Solutions

 

Problem 1: 320 times 25

 

Solution: 25 is one-quarter of 100. 320 times 100 equals 32,000. Divide by 4 to get 8,000.

 

Problem 2: 480 times 75

 

Solution: 480 times 75 equals 480 times 100 times 0.75. 48,000 times 0.75 equals 36,000.

 

Problem 3: 1,250 times 80

 

Solution: 1,250 times 8 equals 10,000. Multiply by 10 to get 100,000.

 

Problem 4: 4,500 divided by 15

 

Solution: Divide both numbers by 5 to simplify. 900 divided by 3 equals 300.

 

Problem 5: 12,000 divided by 240

 

Solution: Cancel a zero from each. 1,200 divided by 24 equals 50.

 

Problem 6: 8,400 divided by 35

 

Solution: 8,400 divided by 7 equals 1,200. 1,200 divided by 5 equals 240.

 

Aim for under 60 seconds per problem. Practice writing each step on paper so you can sense-check your work, the same way you would in a live interview.

 

How Should You Drill Growth Rates and CAGR?

 

Drill growth rates and CAGR using the Rule of 72, which tells you how many years it takes for a value to double given an annual growth rate. The formula is simple: 72 divided by the annual growth rate equals years to double. A business growing at 9% per year will double in 8 years, and a market growing at 6% per year will double in 12 years.

 

Growth rate problems often appear inside growth strategy cases where you must project market size or revenue forward to inform a strategic recommendation. Master the Rule of 72 and you can answer 80% of growth math questions without doing complex compound interest calculations.

 

Growth and CAGR Drill Problems with Solutions

 

Problem 1: Revenue grew from $50 million to $65 million in one year. What is the growth rate?

 

Solution: Growth is $15 million on a base of $50 million. 15 divided by 50 equals 30%.

 

Problem 2: A company's revenue is $100 million and growing at 10% per year. How long until it reaches $200 million?

 

Solution: Apply the Rule of 72. 72 divided by 10 equals 7.2 years.

 

Problem 3: A market is $500 million today and growing at 8% per year. What will it be in 9 years?

 

Solution: 72 divided by 8 equals 9 years to double. The market will be $1 billion in 9 years.

 

Problem 4: Sales grew from 200 units to 320 units. What is the growth rate?

 

Solution: Growth is 120 units on a base of 200. 120 divided by 200 equals 60%.

 

Problem 5: If price increases 10% and volume drops 5%, what is the net revenue change?

 

Solution: Revenue change factor equals 1.10 times 0.95, which is 1.045 or +4.5%.

 

Problem 6: A company grows at 12% per year. How long until it doubles?

 

Solution: 72 divided by 12 equals 6 years.

 

How Should You Drill Breakeven and Profitability?

 

Drill breakeven analysis and profitability problems because they combine arithmetic with business logic, which is where most candidates lose points. Every pricing case, new product case, and investment case will involve some version of breakeven analysis. These drills separate candidates who barely passed undergrad finance from those who can think like a consultant.

 

Memorize these two formulas:

 

• Breakeven units equals fixed costs divided by (price per unit minus variable cost per unit)

 

• Profit equals (price minus variable cost) times quantity, minus fixed costs

 

Breakeven and Profitability Drill Problems with Solutions

 

Problem 1: A product sells for $50, has variable costs of $30, and the company has $400,000 in fixed costs. What is the breakeven volume?

 

Solution: Contribution margin per unit equals $50 minus $30, or $20. Breakeven equals $400,000 divided by $20, which is 20,000 units.

 

Problem 2: A company sells 100,000 units at $25 each. Variable cost is $15 per unit. Fixed costs are $500,000. What is profit?

 

Solution: Contribution margin equals ($25 minus $15) times 100,000, or $1,000,000. Profit equals $1,000,000 minus $500,000, which is $500,000.

 

Problem 3: A new product requires a $2 million investment. It earns $400,000 in annual profit. What is the payback period?

 

Solution: Payback equals $2 million divided by $400,000, or 5 years.

 

Problem 4: A subscription costs $20 per month to deliver and sells for $50 per month. Customer acquisition cost is $300. How many months until breakeven?

 

Solution: Monthly contribution equals $50 minus $20, or $30. Months to breakeven equal $300 divided by $30, which is 10 months.

 

Problem 5: A factory has fixed costs of $1 million and sells widgets at $40 with variable cost of $25. How many widgets must be sold to break even?

 

Solution: Contribution per unit equals $40 minus $25, or $15. Breakeven equals $1 million divided by $15, which is 66,667 units.

 

Problem 6: A SaaS product earns $1,200 per customer per year in profit. Customer acquisition cost is $3,000. What is the payback period?

 

Solution: Payback equals $3,000 divided by $1,200, or 2.5 years.

 

Practice these drills with a stopwatch. Aim for under 90 seconds per problem. The breakeven analysis questions you see in real interviews will follow the exact same patterns.

 

How Should You Drill Market Sizing?

 

Market sizing drills test your ability to estimate the size of a market using assumptions and rapid arithmetic. These problems combine all the previous drill categories into a single estimation chain. Spend at least 3 to 5 minutes per market sizing drill so you can practice structuring the approach before doing math.

 

The standard approach is top-down. Start with a large population number, segment it down using percentages, then multiply by an average price or quantity to reach your final estimate. Always state your assumptions out loud before starting calculations.

 

Market Sizing Drill Problems with Solutions

 

Problem 1: What is the annual market size for coffee shops in the United States?

 

Solution: US population is 320 million. Assume 60% drink coffee regularly, giving 190 million coffee drinkers. Assume each spends $5 per coffee shop visit and visits twice per week, or 100 times per year. 190 million times $5 times 100 equals $95 billion.

 

Problem 2: How many tennis balls are sold in the United States each year?

 

Solution: 320 million people. Assume 5% play tennis, giving 16 million players. Each uses 20 balls per year. 16 million times 20 equals 320 million balls.

 

Problem 3: What is the annual market for toothbrushes in the United States?

 

Solution: 320 million people. Assume 90% brush their teeth and 75% use manual brushes, giving 216 million users. Each uses 4 brushes per year at $3 each. 216 million times 4 times $3 equals $2.6 billion.

 

Problem 4: How many pizzas are sold in New York City each year?

 

Solution: Population is 8 million. Assume each person eats pizza 30 times per year, giving 240 million pizza orders. At an average of 3 people per pizza, that is 80 million pizzas.

 

Problem 5: What is the annual market for haircuts in the United States?

 

Solution: 320 million people. Assume 90% get professional haircuts, giving 290 million. Average frequency is 8 cuts per year at $25 each. 290 million times 8 times $25 equals $58 billion.

 

Problem 6: How many cars are sold in the United States each year?

 

Solution: There are roughly 280 million cars in the United States. Average car life is 14 years. Annual sales equal 280 million divided by 14, or 20 million cars.

 

What Daily Routine Should You Follow for Math Drills?

 

Follow a daily routine of 20 to 30 minutes of timed math drills for 2 to 3 weeks before your first live case interview. Five 25-minute sessions per week beats one 3-hour session. Consistency builds the automatic recall that drills are designed to create.

 

Here is the daily routine I recommend to coaching clients:

 

• Minutes 0 to 5: Mental warm-up. Do 10 quick percentage problems to wake up your brain.

 

• Minutes 5 to 15: Targeted category drilling. Pick one of the five categories and do 8 to 10 problems with a stopwatch.

 

• Minutes 15 to 22: Multi-step problems. Do 3 to 4 problems that combine two or more skills.

 

• Minutes 22 to 25: Review errors. Identify your slowest or wrong answers and redo them.

 

Week	Focus	Daily Time	Target Accuracy
Week 1	Percentages and basic arithmetic	20 minutes	85%
Week 2	Growth, CAGR, and breakeven	25 minutes	90%
Week 3	Market sizing and mixed drills	30 minutes	95%

 

Track your time and accuracy in a simple spreadsheet. You should see consistent improvement week over week. If you plateau, change your drill mix or slow down to focus on the technique you keep getting wrong.

 

What Are the Most Common Mistakes During Math Drills?

 

The most common mistake candidates make during math drills is practicing without a timer. Untimed practice builds knowledge but not speed, and speed is what interviewers grade you on. Roughly 70% of candidates who fail MBB math fail because they never trained under time pressure during practice.

 

Here are the seven mistakes that hold candidates back:

 

• Practicing without a stopwatch. Without time pressure, you never build the speed needed for live interviews. Always use a timer.

 

• Skipping the units. Dropping million, billion, or per year is the number one quant error in real cases. Always write units next to every number.

 

• Rounding too aggressively. Some candidates round 320 million to 300 million, then round again to 290 million, and end up far from the right answer. Round once, at the start, then commit.

 

• Doing the math in your head only. Even experienced consultants write out their calculations on paper. Drilling in your head trains a habit that breaks under pressure.

 

• Skipping the sense check. After every drill, ask yourself if the magnitude makes sense. If you calculated that a small business has $50 trillion in revenue, you missed a zero somewhere.

 

• Practicing only one category. Candidates love drilling what they are already good at. Drill your weakest category first every day.

 

• Stopping when it gets hard. The drills you fail are the drills that teach you the most. When you miss a problem, redo it three times before moving on.

 

Avoid these mistakes and your accuracy will climb 20 to 30 percentage points within two weeks.

 

What Are the Best Tools and Resources for Math Drills?

 

The best tools for case interview math drills are the ones that give you instant feedback, timed problems, and progress tracking. You do not need expensive software. A timer, paper, and a structured problem bank are enough. Pair these with a consulting math cheat sheet so you have every formula at hand while you train.

 

Here are the tools and resources to use:

 

• Paper drills with a stopwatch. The simplest and most effective method. Write each problem out, time yourself, check your answer, and log your error rate.

 

• Khan Academy. Free and excellent for refreshing arithmetic, percentages, and fractions if you have not used these skills since high school.

 

• Mental math mobile apps. Several free apps offer timed addition, subtraction, multiplication, and division drills. These build raw calculation speed in 5-minute bursts.

 

• MBA casebooks. Most schools publish casebooks with full case interviews you can use to practice math in context. They are usually free with a quick search.

 

• Recorded mock interviews. Recording yourself solving problems out loud and listening back reveals filler words, hesitation, and unclear steps better than any tool.

 

If you want to learn case interview math quickly with structured drills built into a full prep system, my case interview course walks you through proven strategies in as little as 7 days.

 

How Should You Communicate Math During Drills and the Interview?

 

Communicate your math by verbalizing the formula, walking through the calculation step by step, and ending with a one-sentence business interpretation. Silent math is invisible math, and invisible math gets graded as wrong even when the number is right. Top candidates talk through every step the way a consultant explains analysis to a client.

 

Use this four-step verbalization pattern when you drill:

 

• Step 1: State the formula. Say out loud, To find market share I will divide our revenue by total market revenue.

 

• Step 2: Plug in the numbers. Say, Our revenue is $240 million and total market is $2 billion.

 

• Step 3: Do the math. Say, 240 divided by 2,000 equals 0.12, or 12%.

 

• Step 4: Interpret. Say, So our client holds 12% of the market, which is roughly a top-three position.

 

Practice every drill out loud. Recording yourself on your phone and listening back is the fastest way to spot rambling, hesitation, and unclear steps. Your interviewer should be able to follow every word without asking you to repeat anything.

 

Case Interview Math Drill Tips

 

Tip #1: Drill daily, not in bursts

 

Twenty minutes a day for 14 days beats six hours on a Saturday. Mental math is a muscle, and muscles need consistent stimulus to grow.

 

Tip #2: Always time yourself

 

Every drill should have a target time. If you are not under the target, slow down on technique first, then build speed.

 

Tip #3: Drill your weakest category first

 

Most candidates avoid the math they hate. Reverse this and start every session with your worst category for 5 minutes before doing anything else.

 

Tip #4: Write everything down

 

Use paper for every calculation, even if you can do it in your head. The habit transfers directly to your interview, where written work helps you and your interviewer follow along.

 

Tip #5: Round once at the start

 

Pick clean numbers before you begin the calculation, then commit. Re-rounding mid-calculation introduces compounding errors that destroy your final answer.

 

Tip #6: Sense check every answer

 

Ask if the magnitude makes sense before you state the answer. A 5-second sanity check at the end of every drill prevents the costliest mistakes.

 

Tip #7: Mix drill categories every third day

 

Pure category drills build skill. Mixed drills build the cognitive flexibility you need when an interviewer jumps between math types in a single case.

 

Tip #8: Replay your errors

 

Keep a notebook of every problem you missed. Redo each one three times the next day. Errors are the highest-value drills you will do.

 

Tip #9: Verbalize every drill out loud

 

Silent math in practice creates silent math in interviews. Talk through every calculation as if a McKinsey partner were sitting across from you.

 

Tip #10: Stop when you hit 95% accuracy

 

Once you can solve drills in your target time with 95% accuracy, stop pure drilling and move to math inside full case interview practice.

 

Frequently Asked Questions

 

How long should I drill case interview math each day?

 

Drill for 20 to 30 minutes per day, five days a week, for 2 to 3 weeks before your first live interview. Less than 20 minutes does not build enough reps, and more than 45 minutes causes fatigue and poor retention. Consistency beats volume every single time.

 

How fast should I be able to solve case math drills?

 

Aim for under 30 seconds on percentage problems, under 60 seconds on multiplication and division, and under 90 seconds on breakeven and profitability problems. Market sizing drills should take 3 to 5 minutes including structuring the approach. If you cannot hit these times after 2 weeks of daily practice, focus on technique before speed.

 

Do I need to memorize formulas to drill case math effectively?

 

Yes. Memorize roughly 10 to 15 core formulas including profit, gross margin, breakeven, CAGR, and the Rule of 72. Without these locked into memory, every drill becomes a formula lookup instead of a speed exercise.

 

Are case interview math drills different at McKinsey vs BCG and Bain?

 

The math content is the same across MBB. The difference is in precision. McKinsey tends to expect tighter precision and less rounding, while BCG and Bain allow more aggressive rounding as long as you sense-check the answer. Drill for precision so you are ready for either approach.

 

Can I drill case math without a partner?

 

Yes. Pure math drills are designed for solo practice and only require a problem bank, a stopwatch, and paper. Partner practice becomes important when you move from isolated drills to full case interviews where math is just one step in a longer problem.

 

What is the fastest way to improve case interview math?

 

The fastest improvement comes from drilling your weakest category daily, verbalizing every problem, and logging every error. Most candidates plateau because they keep drilling the same skills they already have. Reverse this by spending 70% of your time on your weakest area until it becomes a strength.

 

When should I stop drilling and move to full case practice?

 

Stop pure drills once you hit 95% accuracy on timed problems across all five categories. At that point, integrate math into full case interview practice so you can train the structure, math, and communication together.

 

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