What the math looks like in Casey
Prep sites that collect candidate reports agree on the format: usually 8 to 10 questions in one case, a mix of multiple choice, numeric entry with unit or rounding instructions, and short written answers, plus tables and charts that several questions draw on. Answers are final, so there's no going back to fix a number. BCG gives the whole case about 30 minutes on its Mexico page and about 35 minutes on its US page.
Neither BCG nor the prep sites publish a list of calculation types. The numeric questions candidates describe are standard case math: sizing a market from survey percentages, revenue, contribution and profit, break-even, growth rates, margins, payback and weighted averages, often read off an exhibit. None of it goes past school arithmetic. The points are lost on picking the wrong formula, the wrong row or the wrong unit.
Prep sites agree you can use your own calculator and that none is provided on screen. Have one you've used this week, plus paper for a running list of every number you work out, with its unit, because later questions reuse earlier answers.
The formulas are in a table on the Casey guide, with a complete worked case. The problems below are new ones, grouped by type. Try each before reading the working.
Market sizing and revenue
Problem 1: a chain of survey percentages
Brightwell rents e-bikes on monthly subscriptions and is looking at Carrowmore, a city of 1.2 million adults. A survey says 40% of adults commute more than 5 km. Of those, 12% would consider an e-bike subscription. Of those who'd consider it, one in three would pay $45 a month.
Casey asks: how many Carrowmore adults would subscribe at $45 a month?
1,200,000 × 0.40 = 480,000 long commuters. 480,000 × 0.12 = 57,600 who'd consider it. 57,600 ÷ 3 = 19,200. Answer: 19,200.
The trap: applying every percentage to the whole city. 12% of 1.2 million, divided by 3, gives 48,000, two and a half times too many. In a chain like this, "of those" means multiply the last result, not the starting population.
Problem 2: revenue in the right unit
Brightwell expects to sign up 25% of those 19,200 in year one. Because sign-ups are spread across the year, the average subscriber pays for 7 months in year one.
Casey asks: what is year-one subscription revenue, in $ millions to one decimal place?
Subscribers: 19,200 × 0.25 = 4,800. Revenue: 4,800 × $45 × 7 = $1,512,000. In millions that's 1.512, which rounds to 1.5. Answer: 1.5.
The trap: using 12 months. 4,800 × $45 × 12 = $2,592,000, or 2.6, and it looks right because a full year feels natural. The second trap is the box: 1512000 and 1.51 are both wrong answers to "$ millions to one decimal place".
Contribution, break-even and pricing
Problem 3: contribution margin from an exhibit
Kettleby Roasters sells coffee to cafés in 1 kg bags at $21. Casey shows the cost per kg:
| Cost per kg | $ |
|---|---|
| Green beans | 9.00 |
| Roasting energy | 1.50 |
| Packaging | 1.10 |
| Delivery | 2.40 |
| Roastery rent (fixed, allocated per kg) | 1.20 |
Casey asks: what is the contribution margin per kg, as a percentage of price to one decimal place?
Variable costs: 9.00 + 1.50 + 1.10 + 2.40 = $14.00. Contribution: $21.00 − $14.00 = $7.00. As a percentage: 7 ÷ 21 = 33.33%. Answer: 33.3.
The trap: including the rent. It sits in the same table in dollars per kg, but it's a fixed cost spread over current volume, and it doesn't change if Kettleby sells one more bag. Counting it gives $5.80 and 27.6%.
Problem 4: break-even and profit
Kettleby is considering a second roasting line with $250,000 a year in fixed costs. Contribution stays at $7 per kg.
Casey asks: how many kg a year must the new line sell to break even, and what profit does it make at 40,000 kg?
Break-even: 250,000 ÷ 7 = 35,714.3. Selling 35,714 kg brings in 35,714 × $7 = $249,998, which is $2 short, so the line needs 35,715 kg. Profit at 40,000 kg: 40,000 × $7 = $280,000, less $250,000 = $30,000. Answer: 35,715 kg to break even; $30,000 profit at 40,000 kg.
The trap: rounding break-even down. A break-even volume is a minimum, so any fraction rounds up, unless the box explicitly says "nearest whole number", in which case follow the box.
Problem 5: what a discount really costs
A café chain buys 6,000 kg a year from Kettleby at $21 and asks for 10% off, bringing the price to $18.90. Variable cost stays at $14.00.
Casey asks: by what percentage would the chain's volume need to rise for Kettleby to earn the same total contribution from it? One decimal place.
New contribution: $18.90 − $14.00 = $4.90 per kg. Today's contribution: 6,000 × $7 = $42,000. Volume needed: $42,000 ÷ $4.90 = 8,571.4 kg. Increase: 8,571.4 ÷ 6,000 = 1.4286, a rise of 42.9%. The quicker route is 7 ÷ 4.90 = 1.4286. Answer: 42.9.
The trap: assuming 10% more volume makes up for 10% off the price. The discount comes straight out of contribution: $2.10 off the price is $2.10 off a $7.00 contribution, which is 30% of it.
Growth, mix and exhibits
Problem 6: year-on-year growth and CAGR
Oakhollow Foods makes snacks. Revenue was $40.0 million in 2023, $45.0 million in 2024 and $50.0 million in 2025.
Casey asks: (a) what was revenue growth in 2025, and (b) what was the compound annual growth rate from 2023 to 2025? Both as percentages to one decimal place.
(a) (50.0 − 45.0) ÷ 45.0 = 5 ÷ 45 = 11.1%. (b) 50 ÷ 40 = 1.25 over two years. The square root of 1.25 is 1.118, so 11.8% a year. Check: 1.118 × 1.118 = 1.2499. Answer: (a) 11.1; (b) 11.8.
The trap: for (a), dividing by the later year gives 5 ÷ 50 = 10.0%. For (b), halving the total growth gives 25% ÷ 2 = 12.5%, which ignores compounding. For more years, CAGR = (end ÷ start) raised to the power 1 ÷ years, minus 1. If your calculator has no power key, test a rate by multiplying it out: 1.118 × 1.118 is quick to check.
Problem 7: a weighted average margin
Oakhollow's 2025 revenue by product line:
| Line | Revenue ($m) | Gross margin |
|---|---|---|
| Crisps | 30 | 40% |
| Nuts | 15 | 25% |
| Bars | 5 | 10% |
Casey asks: what is Oakhollow's overall gross margin?
Gross profit by line: 30 × 0.40 = 12.0; 15 × 0.25 = 3.75; 5 × 0.10 = 0.5. Total 16.25 on revenue of 50. 16.25 ÷ 50 = 32.5%. Answer: 32.5%.
The trap: averaging the three percentages, (40 + 25 + 10) ÷ 3 = 25%. Percentages only average straight when the bases are equal. Weight by revenue. The same logic explains a follow-up Casey could ask: if bars grow faster than crisps, the overall margin falls even when no line's own margin changes.
Problem 8: reading a share exhibit
Casey shows Oakhollow's regional markets:
| Region | Market 2024 ($m) | Share 2024 | Market 2025 ($m) | Share 2025 |
|---|---|---|---|---|
| North | 200 | 10% | 240 | 9% |
| South | 125 | 8% | 144 | 10% |
| West | 125 | 12% | 100 | 14% |
Casey asks: which region added the most Oakhollow revenue from 2024 to 2025, and how much, in $ millions to one decimal place?
Revenue is market × share. North: 20.0 to 21.6, up 1.6. South: 10.0 to 14.4, up 4.4. West: 15.0 to 14.0, down 1.0. Answer: South, 4.4. The regions add up to $45.0 million and $50.0 million, matching problem 6.
The trap: reading share alone. West gained 2 share points and still lost revenue, because its market shrank by 20%. North lost a point and still grew, because its market grew by 20%. Also watch points against percent: South's share rose 2 percentage points, which is a 25% increase in share.
Costs and payback
Problem 9: a percentage of a percentage
Fenwick Linen runs a commercial laundry for hotels. Its operating costs are $5.0 million a year, and labor is 60% of that. An automated sorting system would cut labor costs by 15%.
Casey asks: by what percentage would total operating costs fall, and what is the saving per year?
Labor: $5.0m × 0.60 = $3.0m. Saving: $3.0m × 0.15 = $0.45m. As a share of total costs: 0.45 ÷ 5.0 = 9%. The shortcut is 60% × 15% = 9%. Answer: 9%, or $450,000 a year.
The trap: answering 15%. The cut applies to one part of the cost base, so the effect on the total is smaller.
Problem 10: payback when savings ramp up
The sorting system costs $1.8 million upfront. In year one, savings are half the full rate while staff learn the system. From year two, Fenwick saves the full $450,000 a year.
Casey asks: what is the payback period, in years to one decimal place?
Cumulative savings: year 1, $225,000; year 2, $675,000; year 3, $1,125,000; year 4, $1,575,000. After four years Fenwick is still $225,000 short. Year five saves $450,000, so it takes half of year five. Answer: 4.5.
The trap: $1.8m ÷ $0.45m = 4.0 years, which ignores the slow first year. When the yearly figures aren't flat, add them up year by year until they reach the investment.
Mental math shortcuts
You'll have a calculator, so these aren't about avoiding it. They're for estimating the answer before you type, so a slipped decimal point jumps out, and for ruling out multiple choice options quickly.
- Build percentages from 10%. 15% of 480,000 is 48,000 plus half of that, 24,000, so 72,000.
- Flip awkward percentages. x% of y equals y% of x. 12% of 50 is the same as 50% of 12, which is 6.
- Dividing by 0.8 is multiplying by 1.25. A price of $36 after a 20% discount was $36 × 1.25 = $45 before it. Dividing by 1.25 is multiplying by 0.8; dividing by 0.75 is multiplying by about 1.33; dividing by 0.9 is multiplying by about 1.11.
- Changes don't cancel. Up 10% then down 10% leaves you at 1.1 × 0.9 = 0.99, a 1% fall.
- Rule of 72, as an estimate only. Doubling time is roughly 72 divided by the growth rate in percent. At 8%, about 9 years. Revenue that doubled in 6 years grew about 12% a year; the exact figure is 12.2%. Use it to check a CAGR answer or eliminate an option, never to fill a numeric box.
- Round late. In problem 1, treating one in three as 33% gives 57,600 × 0.33 = 19,008 instead of 19,200. Keep full figures on paper and in the calculator, and round once, at the end, to what the box asks for.
- Drop zeros, then put them back. Work in thousands or millions and write the unit next to every number: "4.8k subscribers", "$1.512m".
- Size-check every answer. If break-even is larger than the whole market, or a margin is above 100%, you've divided the wrong way round.
Units and rounding traps
Prep sites report that Casey's numeric boxes come with instructions on units or rounding. We can't see the exact wording BCG uses, so read each instruction as if it's the only one that matters. These are the conversions that trip people up:
| The box asks for | Your working gives | Type |
|---|---|---|
| $ millions, one decimal place | $1,512,000 | 1.5 |
| $ thousands | $30,000 | 30 |
| Percentage, one decimal place | 0.33333 | 33.3 (or 0.333 only if it asks for a decimal) |
| Units to break even | 35,714.3 kg | 35,715 (a minimum rounds up) |
| Change in revenue, $ millions | 15.0 to 14.0 | −1.0 (the minus sign matters when it asks for the change) |
| Years, one decimal place | 4.5 years | 4.5 |
- Units first. Before you calculate, write the unit the box wants at the top of your working.
- One decimal place means one. 1.51 isn't 1.5 to a strict checker. Round a 5 up: 2.45 becomes 2.5.
- Percent signs. If the box shows a % sign next to it, type the number only: 33.3, not 33.3%.
- Per month or per year. Subscription and staffing questions often mix them. Say the time unit out loud when you write it down.
For numerical practice with a timer, the numerical section of our Bain practice uses similar business math (percentages, growth, margins, reading tables) and is available now, with one free set. It's written for Bain's tests, not Casey. Dedicated BCG practice isn't built yet.
FAQ
What kind of math is in BCG Casey?
Neither BCG nor prep sites publish a list. The numeric questions candidates describe are standard business case math: market sizing from percentages, revenue, contribution and profit, break-even, growth rates, margins, payback and weighted averages, usually tied to a table or chart in the case.
Can I use a calculator for Casey?
Prep sites agree you can use your own calculator and that none is provided on screen. Use one you already know well, and keep pen and paper for a running list of numbers.
Is the math in Casey hard?
The arithmetic is school level. The difficulty is choosing the right numbers from an exhibit, applying percentages to the right base, and entering the answer in the unit and rounding the box asks for, all with no way to go back.
Do answers need to be exact?
BCG doesn't publish how answers are scored or any pass mark. Prep sites report that numeric boxes come with unit and rounding instructions, so the safe assumption is that an answer in the wrong unit or with the wrong rounding counts as wrong.
Are wrong answers penalized in Casey?
It's disputed. One prep site contradicts itself on this across two of its own pages, and BCG doesn't say. Since answers are final either way, work each question carefully once rather than rushing.
How should I practice Casey math in a week?
Do twenty or so problems like the ones above on paper with your own calculator, timed at about three minutes each including reading. Mark every answer against the unit and rounding you'd been asked for, not only the math.
Keep going
The full format and a complete worked case: the BCG Casey guide. The last step of the case: how to give the Casey final recommendation. Back to the BCG online assessment overview, which covers the tests other offices use instead.
Sources we checked: BCG's careers pages for Mexico and the United States (case length), and prep-site reports from MyConsultingCoach, IGotAnOffer, Hacking the Case Interview, MConsultingPrep, Road to Offer and CaseStudyPrep.ai (question types, calculator, answers being final, rounding instructions, scoring).
SolveForge is an independent practice tool and is not affiliated with, endorsed by, or connected to Boston Consulting Group or HireQuotient. Every problem on this page was written by us; none is a real test item or based on one. "BCG" and "Boston Consulting Group" are trademarks of their owner. Nothing here guarantees any assessment result.