Case Interview Math Practice: 30 Drills with Full Worked Solutions

Case interview math practice means drilling the five quantitative categories that appear in nearly every McKinsey, BCG, and Bain interview: percentages, break-even analysis, compound growth (CAGR), market-sizing chains, and profitability bridges. Calculators are not permitted at any MBB firm — candidates must complete each calculation step in roughly 10 seconds on paper, according to Management Consulted.

This drill bank gives you 30 timed problems across all five categories, each with a full worked solution and a business interpretation.

Math in case interviews is usually simple arithmetic. The hard part is speed and composure under pressure. You will not fail because the math is too advanced. You will fail because you blanked on how to find 15% of 240 while a partner stared at you.

The goal of this drill bank: get your hands moving before your brain freezes. Every drill includes the formula, the calculation steps, the answer, and a one-line business interpretation, because in a real case, a number without context is worth nothing.

How to Use This Drill Bank

For each problem below, follow this four-step process before revealing the answer:

1. Write the formula first. Even for simple percentages, writing "X% of Y = ?" keeps you structured.
2. Keep units on every line. Dollars, units, millions. If you drop the units, you will mix millions and billions (the #1 quant error in cases).
3. Calculate in chunks. Break the problem into smaller steps rather than trying to do it all at once.
4. Sanity-check the result. Does the magnitude make sense? Is the direction correct?

This is the same process top candidates use in live McKinsey, BCG, and Bain interviews. According to Management Consulted's fast math guide, the four-step approach — review the data, structure your approach, calculate, drive to insight — prevents the majority of errors candidates make under pressure. It takes 5 extra seconds per calculation and prevents most errors.

Key Formulas You Need

Before diving into drills, make sure you have these formulas locked in. The mental math article covers shortcuts for executing them quickly.

Percentage Calculation

X% of Y = (X / 100) x Y

The fastest approach: use 10% and 1% as anchors and build from there. 15% = 10% + 5%. 8% = 10% - 2%. This is faster than dividing by 100 every time.

Break-Even Formula

Break-even Volume = Fixed Costs / (Price - Variable Cost per Unit)

The denominator (Price - Variable Cost) is called the contribution margin per unit. It represents how much each sale contributes toward covering fixed costs. Once you sell enough units to cover all fixed costs, every additional unit is pure profit.

This formula appears in pricing cases, new product launches, and investment evaluations. If you see fixed costs and per-unit economics in a case, break-even is almost always the right tool. For deeper pricing analysis, see our pricing strategy cases guide.

CAGR and the Rule of 72

Rule of 72: Years to double = 72 / Annual Growth Rate (%)

This is the fastest way to estimate compound growth in your head. At 6% growth, doubling takes 72/6 = 12 years. At 12% growth, doubling takes 72/12 = 6 years.

It also works in reverse: if a market doubled in 9 years, the implied CAGR is roughly 72/9 = 8%.

For more precise CAGR calculations, the exact formula is: CAGR = (End Value / Start Value)^(1/n) - 1. But in a case interview, the Rule of 72 plus mental interpolation is sufficient. See how this applies in growth strategy cases.

Revenue Effect of Price and Volume Changes

Revenue Change Factor = (1 + Price Change %) x (1 + Volume Change %)

When price changes 10% and volume changes -5%, the net revenue effect is 1.10 x 0.95 = 1.045, or about +4.5%. This multiplicative relationship is critical for profitability framework cases.

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Drill Set A: Percentages (10 Drills)

Percentage calculations are the foundation of every case. You will use them to compute margins, growth rates, market shares, and cost breakdowns. If you can only drill one category, drill this one.

Drill Set B: Break-Even and Pricing (8 Drills)

Break-even and pricing math separates prepared candidates from unprepared ones. These problems require you to combine formulas with business logic. Every pricing case, new product case, and investment case will involve some version of break-even analysis. For the full pricing framework, see pricing strategy cases.

Drill Set C: Market-Sizing Chains (7 Drills)

Market-sizing math is multiplication with large numbers. The challenge is not the arithmetic itself. The challenge is keeping zeros straight and sanity-checking whether the result is plausible. For the full market sizing framework (segmentation, assumptions, and sanity checks), see market sizing step-by-step.

Drill Set D: Profitability Bridges (5 Drills)

Profitability drills combine percentages with business logic. These are the calculations that appear in nearly every profitability and cost-optimization case. For the full diagnostic framework, see profitability framework.

Test Your Understanding

Test yourself

1 / 4

Question 1 of 4

A product has a price of $100, variable cost of $60, and fixed costs of $800K. What is the break-even volume?

• A8,000 units
• B13,333 units
• C20,000 units
• D80,000 units

Common Quant Errors (And How to Fix Them)

These four mistakes account for the vast majority of math errors in live case interviews. Each one is preventable with a specific habit.

1. Dropping Zeros and Units

This is the most common error by far. Candidates write "30" when they mean "30M," or confuse millions and billions mid-calculation.

Example of the error: The interviewer says "revenue is $2.4 billion and costs are $1.8 billion." The candidate writes "2.4 - 1.8 = 0.6" and then says "profit is $600,000." The candidate dropped six zeros.

The fix: Write the unit suffix (M, B, K) on every single number, every single line. Say it out loud: "Revenue is $2.4B minus costs of $1.8B equals $600M in profit." When you multiply numbers with different unit scales (e.g., 50K stores x $200K revenue), convert to a common unit first: 50K x $200K = 50 x 200 x K x K = 10,000 x K^2 = 10,000M... this is where it gets confusing. Instead, write: 50,000 x $200,000 = $10,000,000,000 = $10B. Or think of it as: 50K stores at $0.2M each = $10B. Pick the approach that keeps you cleanest.

2. Doing Mental Math Without Writing Structure

Trying to hold intermediate steps in your head under interview pressure is a recipe for errors. Your working memory is already taxed by case structure, hypothesis tracking, and communication.

Example of the error: The interviewer asks "what is 15% of $420M?" The candidate stares at the ceiling for 8 seconds, then says "$63M" with visible uncertainty. Even if the answer is correct, the interviewer cannot follow the reasoning and cannot help if you go off track.

The fix: Write every step on paper, and narrate as you go. "I'll find 10% first, that is $42M. Then 5% is half of that, $21M. So 15% is $42M plus $21M, which is $63M." This takes 5 extra seconds and makes you look structured rather than uncertain. Management Consulted's case math guide emphasizes that narrating your math out loud is one of the strongest signals of a well-prepared candidate. Hacking the Case Interview similarly notes that candidates who show their work step-by-step allow the interviewer to identify and correct errors, which is actually a positive signal — it demonstrates intellectual humility and collaborative problem-solving.

3. Solving for Exact Precision When a Rounded Answer Is Enough

Spending 30 seconds computing 17.3% of $847M to two decimal places is wasted time. The interviewer does not need $146.531M. They need "roughly $150M" delivered in 5 seconds.

Example of the error: "What is 23% of $780M?" The candidate laboriously calculates: "23 times 780... 20 times 780 is 15,600... 3 times 780 is 2,340... total is 17,940... so $179.4M." This took 20 seconds.

The fix: Round the inputs. "23% of $780M, I'll round to roughly 25% of $800M, which is $200M. Adjusting down slightly for the rounding, approximately $180M." This took 5 seconds and the answer is within 1% of exact. In case interviews, speed and direction matter more than precision. According to CaseInterview.com, interviewers expect quick, directionally correct math, not perfect arithmetic. IGotAnOffer's case math guide agrees: a clear, rounded estimate with stated assumptions scores higher than a slow precise answer that loses the thread of the argument.

4. Giving Numbers Without Business Implication

This is not a math error. It is a communication error. But it is the one that costs candidates the most points, because interviewers interpret a naked number as a lack of business judgment.

Example of the error: After calculating that market size is $2.8B, the candidate says "So the market is $2.8 billion" and stops, waiting for the next question.

The fix: Always add one sentence of interpretation. "So the market is roughly $2.8B. At our target share of 5%, that is $140M in revenue, which is large enough to justify the $30M investment the client is considering. The payback would be under 3 years." This transforms a calculation into an insight. For more on translating numbers into recommendations, see our guide on case interview synthesis.

15-Minute Daily Routine

Consistency beats marathon sessions. Here is a practical routine based on how candidates who successfully land MBB offers describe their prep:

Minutes 1-5: Percentages. Pick 3-4 drills from Set A above. Time yourself. Target: under 10 seconds per calculation.

Minutes 6-10: Break-even or pricing. Pick 2-3 drills from Set B. These take longer because they require setup. Target: under 30 seconds per problem including the business interpretation.

Minutes 11-15: One market-sizing chain plus one synthesis statement. Pick one drill from Set C. Do the full multiplication chain, sanity-check the result, and practice stating what the number means for a business decision.

Track your times over days. You should see noticeable improvement within one week. If a category is not improving, go back to the mental math techniques article and review the relevant shortcut.

For a consolidated drill page with 30 timed problems and instant grading, use our free case interview math practice page — same skills, purpose-built for speed work.

For a complete prep schedule that integrates math practice with frameworks, casing, and behavioral prep, see our consulting interview prep timeline.

Sources and Further Reading (checked March 10, 2026)

• McKinsey case interview preparation (calculator policy): https://www.mckinsey.com/careers/interviewing
• BCG case interview preparation (quantitative expectations): https://careers.bcg.com/global/en/case-interview-preparation
• Bain case interview prep: https://www.bain.com/careers/interview-prep/
• IGotAnOffer, case interview math guide: https://igotanoffer.com/blogs/mckinsey-case-interview-blog/case-interview-maths
• Hacking the Case Interview, comprehensive math guide: https://www.hackingthecaseinterview.com/pages/consulting-case-interview-math
• Management Consulted case math guide (10-second calculation standard, four-step approach): https://managementconsulted.com/case-interview-math/
• Management Consulted fast math guide: https://managementconsulted.com/fast-math/
• RocketBlocks consulting drills and quantitative practice: https://www.rocketblocks.me/consulting.php
• CaseInterview.com math and case resources: https://www.caseinterview.com/
• GMAT Club mental math and quantitative references: https://gmatclub.com/
• McKinsey Quarterly, "The Power of Pricing" (on the relationship between pricing math and operating profit): https://www.mckinsey.com/capabilities/growth-marketing-and-sales/our-insights/the-power-of-pricing

Related Guides

• Mental Math for Case Interviews
• Market Sizing Step-by-Step
• How to Practice Case Interviews
• Case Interview Examples