Case Math Drills
Practice business calculations with real case interview scenarios.
Need formulas? See our complete case math guide →
Topic
Difficulty
How it works
- Answer business scenario questions in 3 minutes
- Small tolerance allowed for rounding
- See explanations after each answer
What case math drills actually train
A case interview rarely asks you to compute something. It describes a business situation and leaves you to work out which number would settle the question. The drills above are built around that gap: each one is a generated business scenario with a company, an industry and a set of figures, and your job is to pick the right calculation before you do any arithmetic.
Sessions run 3 minutes. Scenarios are generated fresh from 11 topic areas across three difficulty levels, so there is no fixed question bank to memorise, and every answer is followed by a worked explanation showing the formula and the substitution.
The 11 topic areas
Pick one topic to drill a weakness, or leave it on Mixed to simulate not knowing what is coming:
- Profitability & margins
- Revenue, COGS, gross and operating and net margin, EBITDA, and profit per unit. The default opening of most profitability cases.
- Breakeven analysis
- Fixed versus variable cost splits, contribution margin, breakeven units and revenue, and months to breakeven on an investment.
- Growth & CAGR
- Single-period growth, compounding forward, CAGR backwards out of two endpoints, decline rates, and growth captured through market share.
- ROI & payback
- Return on investment, simple and uneven-cash-flow payback, net return over a multi-year horizon, and the Rule of 72.
- Market sizing
- Top-down population chains, household penetration, usage-based sizing, and backing out a total market from a known share.
- Pricing strategy
- Cost-plus pricing to a target margin, the revenue effect of a price rise against volume loss, and premium pricing off a competitor benchmark.
- Cost reduction
- Savings from fixed cost programmes, per-unit variable cost reductions, and headcount actions.
- Customer economics
- CLV, CAC, churn and the revenue it destroys, and ARPU. The core of any subscription or retention case.
- Capacity utilisation
- Utilisation rates, available headroom, and the revenue unlocked by moving from current to target utilisation.
- Working capital
- Inventory days, cash freed by cutting DSO, and the cash conversion cycle.
- Market share
- Share calculation, the revenue impact of a share point gained or lost, and total market inferred from share.
Every formula these drills use
This is the complete set the generator draws on, with the specific error each one invites. If you learn nothing else, learn the third column.
| Metric | Formula | What trips people up |
|---|---|---|
| Gross margin | (Revenue − COGS) / Revenue | Margin is always over revenue, never over cost. Dividing by cost gives you markup, a different and larger number. |
| Operating margin | Operating income / Revenue | Interviewers switch between gross, operating and net margin mid-case. Ask which one they mean rather than guessing. |
| Contribution margin | Price − Variable cost per unit | Per unit, not in total. The percentage version is 100% − variable cost %. |
| Breakeven units | Fixed costs / Contribution margin | Contribution margin per unit in the denominator. Using total profit instead is the classic slip. |
| Breakeven revenue | Fixed costs / Contribution margin % | Same structure, but the denominator is a percentage, so the answer comes out in currency. |
| Growth rate | (End − Start) / Start | Divide by the starting value. Dividing by the end value understates growth and is very hard to spot afterwards. |
| CAGR | (End / Start)^(1/n) − 1 | n is the number of periods, which is one fewer than the number of years listed. 2021 to 2024 is 3 years, not 4. |
| Future value | PV × (1 + r)^n | Compounding, not multiplication. Three years at 10% is ×1.331, not ×1.30. |
| ROI | (Return − Investment) / Investment | The numerator is the gain, not the gross return. Using gross return inflates ROI by exactly 100 percentage points. |
| Payback period | Investment / Annual cash flow | With uneven cash flows you have to walk the cumulative total year by year and interpolate the final part-year. |
| Rule of 72 | Years to double ≈ 72 / rate | Works in both directions and is the fastest way to sanity-check any compounding answer. |
| Price from target margin | Cost / (1 − margin %) | The most-failed calculation in case interviews. A 20% margin on $80 of cost is $100, not $96. |
| Market size (top-down) | Population × filter % × adoption % × spend | State each assumption out loud. The number matters less than whether the chain is defensible. |
| Total market from share | Company revenue / market share % | A division, not a multiplication. This is the reverse-percentage trap in disguise. |
| Customer lifetime value | Avg order value × orders per year × lifespan | Compare it against CAC. A business with CLV below CAC does not have a growth problem, it has a model problem. |
| Customer acquisition cost | Marketing spend / new customers | New customers only. Including retained customers quietly flatters CAC. |
| Capacity utilisation | Current production / max capacity | Spare capacity is the complement. Incremental volume into spare capacity carries no new fixed cost, which is usually the point of the question. |
| Inventory days | (Avg inventory / COGS) × 365 | COGS, not revenue. Using revenue understates the days because revenue is the larger number. |
| Cash conversion cycle | Inventory days + receivable days − payable days | Payables are subtracted. A negative cycle means suppliers are funding your working capital, which is a good thing. |
| Market share | Company revenue / total market | Check that the two numbers cover the same geography and the same period before dividing. |
The four errors that cost candidates offers
Margin over cost instead of over revenue
Margin is profit divided by revenue. Markup is profit divided by cost. A product costing $80 sold at $100 carries a 20% margin and a 25% markup. Interviewers ask for margin and candidates deliver markup constantly.
Reversing a percentage by multiplying
To undo a 20% discount you divide by 0.8, you do not multiply by 1.2. The first gives $100 from $80; the second gives $96. This single error accounts for more wrong answers than any other in the set.
Counting periods instead of gaps
CAGR from 2021 to 2024 uses n = 3, not 4. Off-by-one on the exponent produces an answer that looks plausible and is wrong, which is the worst combination.
Losing the order of magnitude
Say whether the answer is in millions or billions before computing the digits. An interviewer will let a 5% arithmetic error pass. A 10x error ends the case.
How to use these drills well
Start on Mixed at Foundation to find out where you actually stand, then drill the single topic you scored worst on until it stops being the worst. Do not stay on Mixed indefinitely — it feels productive and it hides weaknesses by averaging them away.
Read every explanation, including the ones for questions you got right. Getting the right answer by a slower route is still a problem when you are on a clock in front of a partner.
Build the underlying speed with mental math sprints, add brain teasers for logic and estimation, and use a study plan to sequence the whole thing.
Frequently asked questions
How long is a case math drill?
Each session runs for 3 minutes. You work through as many business scenarios as you can in that window, and after every answer you get a step-by-step explanation of the correct approach before moving on.
How is this different from the mental math sprint?
The mental math sprint gives you a bare calculation and times you. Case math drills give you a business scenario and make you decide which calculation to run before you can run it. That decision is the part real interviews test, and it is the part pure arithmetic practice never touches.
Do I have to be exactly right?
No. Every question carries a tolerance band, because case interviews are judged on being close and defensible rather than on decimal precision. Rounding sensibly is a skill the drills reward rather than punish.
What are the difficulty levels?
Foundation covers single-step calculations with clean numbers. Standard matches what a typical first-round case asks. Advanced chains several steps together with awkward figures, which is closer to a final round or a partner case.
Which topics come up most often in real case interviews?
Profitability and breakeven dominate, followed by growth and market sizing. Customer economics has become far more common as consulting work has shifted towards subscription and digital businesses. Working capital and capacity show up mainly in operations and turnaround cases.
Is this enough on its own to prepare for a case interview?
No, and it is not meant to be. These drills build the quantitative half. You still need to practise structuring, hypothesis-driven thinking and communication, ideally in live mocks with a partner. What the drills do is make sure the maths is never the thing that costs you the offer.
Is it free?
Yes, entirely, and no account is needed. An optional free account saves your history across devices and tracks which topics you keep getting wrong.