In a first-round case, the interviewer is rarely grading whether you can multiply. They are grading whether you set the equation out loud, keep units attached, and say what the number means before anyone asks. Most candidates train the opposite skill: silent speed on a phone calculator, then freeze when the firm bans electronics. After this hub you will know which CoachNed guide and drill to open for each leak, how firms actually talk about calculators, and a four-week plan that builds floor accuracy instead of peak arithmetic.
This page is the curated map of every live case-math article and drill on CoachNed. Use the tables like a gym board: pick the skill you leaked last, run the timed rep, then return to a full case.
What the sheet actually rewards
I score math as three separate marks: setup, arithmetic, and so-what. Setup is stating the identity and the units before any digits. Arithmetic is the chain with a rounding rule you announce. So-what is one sentence that answers the case question with the number you just produced. A silent correct product with no setup usually loses the same points as a loud wrong product with a clean tree — the sheet treats both as evidence you cannot run a workstream.
Ned's rule. Announce the rounding rule before the first multiply. "I will keep two significant figures until the last step, then check direction" tells me you own the error budget. Silent rounding looks like guessing.
What the firms say about calculators and accuracy
Read the invitation for your assessment. The live room and the online screen are not the same rulebook.
McKinsey's Beautify practice case states, in plain language, that calculators are not allowed and that you should write calculations on paper, talk the interviewer through each step, and take time to plan before punching numbers. The same coaching note appears on GlobaPharm and Diconsa. Separately, McKinsey's Problem Solving Test coaching guide tells candidates they cannot bring a calculator and that many items are designed so a rough estimate eliminates wrong options — accuracy under estimation beats spreadsheet precision.
BCG's case interview preparation page lists "perform quick calculations" as part of the interview job, alongside structure and communication. For the older online case practice PDF BCG published for candidates, the firm explicitly allowed a basic calculator but barred spreadsheets — a different tool policy than the interviewer-led room. Treat Casey and CCA as timed, scored math under whatever rules your invite states; do not assume the live case will hand you a device.
Bain's case interview preparation page tells candidates to think aloud and share reasoning and calculations even when unsure, to emphasize key numbers, and to bring pen and paper for in-person interviews. Bain does not advertise a calculator free-for-all in the live case. Prep as if the pen is the tool.
CoachNed is not affiliated with McKinsey, BCG, Bain, or any firm named here.
One arithmetic chain, done the way the room wants
Invented client: HarborLine Ferries, a coastal passenger ferry operator. Question: if HarborLine raises the average ticket by 8% and loses 5% of passengers, does contribution improve?
Given:
- Current passengers: 1.2 million / year
- Average ticket: $42
- Variable cost per passenger: $18
- Fixed costs ignore for this contribution check
Step 1 — identity out loud. Contribution = passengers × (ticket − variable cost). Units: dollars per year.
Step 2 — base contribution. Ticket − VC = $42 − $18 = $24. Passengers ≈ 1.2M. Round passengers to 1.2 × 10^6. Contribution ≈ 1.2 × 24 = 28.8 → $28.8M. Sanity check: 1M passengers at $24 is $24M; 0.2M more is $4.8M; total $28.8M. Direction correct.
Step 3 — new ticket and volume. New ticket = 42 × 1.08. 42 × 1.1 = 46.2; subtract 42 × 0.02 = 0.84; new ticket = $45.36. Round working ticket to $45.4. New passengers = 1.2M × 0.95 = 1.14M.
Step 4 — new unit contribution. 45.4 − 18 = $27.4. New contribution ≈ 1.14 × 27.4. Compute 1 × 27.4 = 27.4; 0.14 × 27.4 ≈ 0.14 × 27 = 3.78, plus 0.14 × 0.4 = 0.056 ≈ 3.84. Total ≈ $31.2M.
Step 5 — so-what. Contribution rises about $2.4M (roughly +8% on the base), so the price move improves contribution under these assumptions. Flag the risk: if elastic passengers are the high-margin day-trippers, the 5% volume loss may be optimistic.
That chain is what I write on the evidence log: setup, rounding announced, sanity check, recommendation tied to the number. Drill the same shape on /drills/math and /drills/quick-math.
Mental arithmetic and estimation
| Guide | Drill or tool | Time target per rep |
|---|---|---|
| Mental math for cases | /drills/quick-math | 60–90 seconds |
| Case math shortcuts | /drills/math | 2–3 minutes |
| Case interview math practice | /drills/quick-math | 10-rep block, 12 minutes |
| How case math is scored | Full case on /start | One scored mini-case |
| CoachNed Quick Math | /drills/quick-math | Free forever, no account |
| Case interview cheat sheet | Pen + timer | 5-minute review before a mock |
Build the floor: percentages of round numbers, multiply by 1.1 / 0.9, and order-of-magnitude checks. Speed without a sanity check is a liability.
Percentages and growth
| Guide | Drill or tool | Time target per rep |
|---|---|---|
| Consulting math formulas | /tools/cagr-calculator | 3 minutes to verify by hand first |
| Case interview formulas | /drills/math | 2 minutes |
| Revenue growth cases | /interview | Full voice case |
| Growth strategy cases | /drills/structure then math | 4 minutes structure + 3 minutes math |
| Driver tree | /drills/math | Attach % to each branch |
CAGR and mix shifts are where candidates invent identities. Write volume × price × mix before you name a CAGR.
Break-even and margins
| Guide | Drill or tool | Time target per rep |
|---|---|---|
| Break-even in cases | /tools/breakeven-calculator | 3 minutes by hand, then check |
| Profitability framework | /drills/math | Isolate one driver in 4 minutes |
| Unit economics | /drills/math | Pick the unit in 60 seconds |
| Customer profitability | /tools/breakeven-calculator | Cost-to-serve check, 5 minutes |
| Capital One case math | Pen + paper | Bank-style break-even, 6 minutes |
Contribution margin before break-even units. If you cannot name fixed versus variable in one breath, stop and re-read the break-even guide.
Market sizing
| Guide | Drill or tool | Time target per rep |
|---|---|---|
| Market sizing step by step | /drills/market-sizing | 6–8 minutes |
| Market sizing questions | /tools/market-size-calculator | Two paths that reconcile |
| Guesstimate questions | /drills/market-sizing | 5 minutes |
| Market sizing resources | /drills/market-sizing | One prompt, two methods |
| Case interview types | /consulting-cases | Name the closing number first |
I stop listening when the sizing tree has no second path. Top-down and bottom-up should land within a factor of two; if they do not, you have a unit error, not a "creative" answer.
NPV and payback
| Guide | Drill or tool | Time target per rep |
|---|---|---|
| NPV in case interviews | /drills/math | Mental NPV strip, 4 minutes |
| ROI and payback | Pen + paper | Payback years, 3 minutes |
| DCF for cases | Scratch paper | Five years + terminal, 8 minutes |
| Cost-benefit analysis | /drills/math | Name the missing cash flow |
Interview NPV is cash timing with a discount rate you state, not a spreadsheet model. Payback often scores higher than a fake precision NPV.
Chart and exhibit reading
| Guide | Drill or tool | Time target per rep |
|---|---|---|
| Case interview exhibits | /drills/charts | 90 seconds to insight |
| MIT Sloan case book | /drills/charts | Quant exhibit pacing |
| Inductive vs deductive | /drills/charts | Claim only what the chart supports |
The insight is never the tallest bar. State the comparison the interviewer needs for the recommendation.
Online tests that score maths
| Guide | Drill or simulator | Time target per rep |
|---|---|---|
| McKinsey Solve | /mckinsey-sea-wolf | Full module under invite timing |
| McKinsey Red Rock | /mckinsey-red-rock | Study then Game under clock |
| Red Rock simulator design | /mckinsey-red-rock | One timed pass |
| BCG Casey | /casey/urbanbrew-coffee-margin-case | ~30 minutes as invited |
| BCG CCA | /tools/bcg-cca-simulator | Full timed numerical set |
| BCG CCA explained | /tools/bcg-cca-simulator | Match the invite |
| Bain SOVA | /bain-sova | Soft timing, consistency |
| Bain TestGorilla | Calculator only if invite allows | Read the trap questions |
| Numerical reasoning tests | /drills/math | SHL / Aon / Sova formats |
| Consulting aptitude tests | /drills/quick-math | Gate clearance, not a grade |
| MBB assessment simulators | Match the invite | One full dress rehearsal |
Online math is often multiple choice under a hard clock. Live case math is collaborative narration. Train both; do not confuse them.
Four-week maths plan
| Week | Focus | Daily load | Pass criterion |
|---|---|---|---|
| 1 | Mental arithmetic + percentages | 15 min on /drills/quick-math; 1 identity from formulas | 8/10 quick-math correct without a phone |
| 2 | Break-even, margins, unit economics | 2 hand break-evens; 1 check on /tools/breakeven-calculator | Setup spoken before digits every time |
| 3 | Market sizing + charts | 1 sizing on /drills/market-sizing; 1 chart on /drills/charts | Two sizing paths within 2× |
| 4 | NPV / payback + assessment dress | 1 payback chain; 1 simulator matching your invite | Timed full pass without tool panic |
If you have an interview in under two weeks, compress weeks 1–2 into four days and spend the rest on the assessment that is actually on your calendar. See also how to practice case interviews and the prep timeline.
Practice this today
Open /drills/quick-math (free forever) and run ten reps out loud with a timer. Then redo the HarborLine chain on paper without a calculator. When that is clean, sit a five-minute first case on /start or a full voice case on /interview. Everything on CoachNed is open for seven days with no card; then $120 for a recruiting season or $49 a month — see /pricing.
Frequently asked questions
Do consulting case interviews allow calculators?
Usually not in the live interviewer-led room. McKinsey's official practice cases say calculators are not allowed and you should work on paper. Some online assessments allow a basic calculator; BCG's published online case practice PDF did. Always follow the rules in your invite.
How accurate does case math need to be?
Close enough that the recommendation does not flip if you are 10% off, and precise enough that units and order of magnitude are correct. McKinsey's PST coaching material emphasizes estimation shortcuts. A perfect product with the wrong identity still fails.
Should I memorize consulting math formulas?
Memorize a short list of identities — contribution, break-even units, CAGR shape, payback — then practice attaching them to a spoken setup. The formulas guide is the checklist; the drills are the training.
How long should market sizing take in a case?
About six to eight minutes for a clean two-path size with a sanity check. Longer is fine if the interviewer is collaborating; shorter is fine if they only want a ballpark for a later exhibit.
What is the fastest way to improve case math in two weeks?
Daily quick-math for accuracy, then break-even and sizing under a timer, then one full case every other day. Skip polishing advanced NPV until your floor arithmetic holds.
Sources
- McKinsey Beautify practice case — no calculators; talk through steps; plan before calculating. Checked 2026-09-24.
- McKinsey GlobaPharm practice case — same calculator and narration coaching. Checked 2026-09-24.
- McKinsey Diconsa practice case — paper calculations; organized approach. Checked 2026-09-24.
- McKinsey Problem Solving Test coaching tips (PDF) — no calculator; approximate to eliminate options. Checked 2026-09-24.
- BCG case interview preparation — quick calculations as part of the case job. Checked 2026-09-24.
- BCG online case practice booklet (PDF) — basic calculator allowed; no spreadsheet; 45-minute timed practice. Checked 2026-09-24.
- Bain case interview preparation — think aloud on calculations; pen and paper for in-person. Checked 2026-09-24.