Most candidates practice case math as one blurry skill called "getting faster." That is how you train yourself to finish wrong. On the scoring sheet I use, a clean setup with a late number still scores; a fast wrong number does not.
The thesis: speed and accuracy are separate grades. Until you measure them apart, every mixed set you run is noise. This page is the practice program — a diagnostic, a four-week schedule with daily minutes, twenty original timed problems with answers by operation, and a scoring method that tells you which muscle to train next. Tips and shortcuts belong elsewhere; formulas with units belong on the formulas guide.
Firms are explicit that quantitative work sits inside a broader problem-solving conversation. BCG asks you to analyze data, perform quick calculations, and identify the important factors. Bain screens many consulting applicants with a digital assessment of roughly 30–40 minutes that probes problem-solving and analytical skill before any case round. The arithmetic is middle-school. The grade is whether you can set it up out loud, finish cleanly, and say what the number means for the client.
What the room actually scores
When you go quiet and start scratching numbers, I am listening for four things, in order:
- The equation, spoken before the arithmetic.
- Units attached to every intermediate.
- A number inside a sensible band (usually ±10% of the exact figure for multi-step items).
- A one-line so-what that uses the number.
I do not care that you once knew calculus. BLS counts over a million management-analyst jobs in the U.S. as of 2024; the day-to-day work is percentages, rates, and contribution math under a clock, not exam algebra. Treat practice as that environment: pen, no calculator, timer visible, answers hidden until you write yours.
Ned's rule. Log two scores every set: accuracy first (setup + final), then speed. Never celebrate a fast wrong answer. Never punish a slow correct setup. Fix the score that is red; ignore the one that is already green.
Day-zero diagnostic (12 minutes)
Print or copy the eight items below. Cover the answer key. Start a 12-minute timer. Say each equation aloud before you compute. Write only the final number and a two-word so-what.
| # | Prompt |
|---|---|
| D1 | What is 18% of $6.5m? |
| D2 | Margin if profit is $22m on $275m revenue? |
| D3 | 1,250 units/day × 280 days × 0.88 utilization — annual output? |
| D4 | Revenue grows from $80m to $104m in three years. Approximate annual growth rate? |
| D5 | Contribution = price $42 − variable $27. Volume 180k. Total contribution? |
| D6 | Fixed costs $4.8m. Contribution $12/unit. Breakeven units? |
| D7 | Market is $2.4bn. Share rises from 8% to 11%. Incremental revenue? |
| D8 | Plant makes 3,600 widgets/hour, runs 7.5 hours/day, 5 days/week. Weekly capacity? |
Diagnostic answer key
| # | Target | Operation tag |
|---|---|---|
| D1 | $1.17m | Percent of base |
| D2 | 8% | Margin |
| D3 | ~308k units (1,250 × 280 × 0.88 = 308,000) | Capacity × util |
| D4 | ~9% per year (rule of 72 / compound estimate; exact CAGR ≈ 9.1%) | Growth |
| D5 | $2.7m | Contribution |
| D6 | 400k units | Breakeven |
| D7 | $72m | Share Δ × market |
| D8 | 135k widgets/week | Multi-step multiply |
Mark each item A (equation right and number within 5%) or M (miss). Then tag the miss with the operation in the table. Your weak group is the tag that appears twice or more. That tag owns Week 1.
If you finished all eight with zero misses but took the full 12 minutes, accuracy is fine and speed is the red score. If you finished in under eight minutes with three misses, you have the opposite problem. Do not "do more cases" until you know which.
How to score speed and accuracy separately
Use this card after every timed set. Do not merge the columns into a single "I felt okay."
| Score | How you measure it | Green | Yellow | Red |
|---|---|---|---|---|
| Accuracy | % of items with correct equation and final within 5% (exact for one-step %) | ≥90% | 70–89% | <70% |
| Speed | Average seconds per item (clock ÷ items attempted) | ≤45s simple / ≤90s multi-step | 46–70s / 91–120s | Above that |
| Setup | Equation spoken before first multiply | Always | Most | Rare |
| So-what | One business sentence using the number | Always | Half | Skip |
Accuracy first. A 100% accuracy / red speed candidate is hireable with two weeks of tempo work. A green speed / red accuracy candidate is failing the sheet even when they feel fluent.
Shock test after every set: pick one finished item, change one input by ±10%, and restate the verdict in one sentence. That is the question partners ask when they are bored of watching arithmetic.
Four-week schedule (daily minutes)
Budget about 15–25 focused minutes on weekdays, plus one longer weekend block. That is enough. The HBS Class of 2025 employment data shows consulting still took 21% of the class at a $190k median base — the competition is dense, but more hours of unfocused math do not beat a tagged miss log.
| Week | Focus | Mon–Fri daily | Weekend (one block) |
|---|---|---|---|
| 1 | Isolate the diagnostic weak tag | 15 min: 8–10 items from that tag only | 30 min: re-run diagnostic; retag |
| 2 | Mixed sets, accuracy locked | 18 min: 10 mixed items; stop if accuracy <90% | 35 min: two 10-item sets with rest |
| 3 | Case-embedded math | 20 min: 6 items that need equation + so-what | 40 min: one full case; pause only to write equations |
| 4 | Pressure + shocks | 20 min: 10 items under Week-2 green times | 40 min: timed set, then shock three inputs |
Daily shape (pick one):
- Accuracy red: 12 minutes on the weak tag, 3 minutes logging miss types, no mixed work.
- Speed red, accuracy green: 10 easy items at a hard clock (40s each), then 5 multi-step at 75s. Misses restart the item, not the set.
- Both yellow: 8 mixed items, grade accuracy first, then check the speed column. Only one becomes "today's lever."
Do not stack this with learning a new case framework in the same hour. Automaticity and structure are different muscles.
Twenty timed problems (answers by operation)
Cover the keys. Run as one 25-minute set (Week 2+) or as four five-item blocks by group (Week 1). No calculator. Answers follow each group.
Group A — percentages and shares (items 1–5)
- 12% of $9.5m
- Price $64, discount 15%. Sale price?
- Costs fall from $40m to $34m. Percent decline?
- Segment is 28% of a $1.8bn market. Segment size?
- Share moves from 14% to 19% of a $620m market. Incremental revenue?
Group A answers: (1) $1.14m (2) $54.40 (3) 15% (4) $504m (5) $31m
Group B — multiply, capacity, throughput (items 6–10)
- 480 × 365
- 480 × 300 operating days
- 2,200 tonnes/day × 310 days × 0.93 uptime
- 55 stores × $2.8m average revenue
- 16 consultants × 1,800 billable hours × $220/hour
Group B answers: (6) 175,200 (7) 144,000 (8) ~635k tonnes (2,200 × 310 × 0.93 = 634,260) (9) $154m (10) $6.336m
Group C — division, rates, breakeven (items 11–15)
- $18.6m ÷ 310 days (daily run-rate)
- 840,000 units ÷ 24 plants
- Fixed $6.0m ÷ contribution $15/unit
- Payback: $3.6m investment ÷ $0.9m annual savings
- Occupancy 82% × 360 rooms × 365 ÷ 2.4 day average stay (approx. annual stays)
Group C answers: (11) $60k/day (12) 35,000/plant (13) 400,000 units (14) 4 years (15) ~45.4k stays (82% × 360 × 365 / 2.4 ≈ 45,360)
Group D — margins, contribution, multi-step (items 16–20)
- Profit $31m on $380m revenue. Margin?
- Price $55, variable $38, volume 210k. Total contribution?
- Revenue $120m, COGS 62%, opex $28m. Operating profit?
- Base year $50m; grow 8% for two years (end of year 2 revenue)?
- Harbor Metals: 1,800 tonnes/day nameplate, 320 planned days, actual uptime 90%. Contribution after energy $7/tonne. Contractor lifts uptime to 95% for +$900k/year. Is it worth it?
Group D answers: (16) ~8.2% (17) $3.57m (18) $17.6m (120 × 0.38 − 28) (19) $58.32m (50 × 1.08²) (20) Planned block = 1,800 × 320 = 576,000 t. At 90%: 518,400 t. At 95%: 547,200 t. Delta = 28,800 t × $7 ≈ $202k contribution. Contractor costs $900k → destroy ~$700k; do not buy.
Item 20 is the one that leaks "so-what." A candidate who multiplies delta tonnes by full price instead of contribution will hire the contractor and fail the case.
Worked practice block: Northline Pack
Use as a single timed item (90 seconds equation, 90 seconds number, 30 seconds so-what).
Facts. Northline Pack runs three filling lines at 4,500 cases/hour each. Lines run 6.5 hours/day, 250 days/year. Current overall equipment effectiveness is 78%. A $2.1m retrofit lifts OEE to 86%. Contribution is $1.40 per case. Variable energy is already in that contribution. Should Northline buy?
Equation. Annual cases = 3 × 4,500 × 6.5 × 250 × OEE. Extra cases = ΔOEE × that planned block. Extra contribution = extra cases × $1.40. Compare to $2.1m (one-year payback test first; multi-year is a second conversation).
Math. Planned block before OEE = 3 × 4,500 × 6.5 × 250 = 21.9375m cases of nameplate-hours. At 78%: ≈ 17.1m. At 86%: ≈ 18.9m. Delta ≈ 1.8m cases. Contribution ≈ 1.8m × $1.40 ≈ $2.5m. Retrofit $2.1m → rough one-year payback, yes on contribution alone.
So-what. Buy if the $2.1m is a one-time capital outlay and OEE actually holds at 86%. Flag volume risk: if demand cannot absorb 1.8m extra cases, the contribution never shows up. That sentence is what the sheet rewards after the multiply.
Practice this today
- Run the day-zero diagnostic under 12 minutes and fill the two-score card.
- Open the weak-tag block from the twenty-item bank and drill only that group.
- Move to live tempo on CoachNed: math drills for case-shaped items, and Quick Math (free forever) for isolated operations.
Everything on CoachNed is open for seven days, no card; then $120 for a recruiting season or $49 a month. When you want the number inside a full conversation, take the five-minute first rep at /start or a live voice case at /interview.
CoachNed is not affiliated with McKinsey, BCG, Bain, Deloitte, or any firm named above.
Frequently asked questions
How long should I practice case math each day?
Fifteen to twenty-five focused minutes on weekdays beats a weekend binge. Use the four-week table above. If accuracy is red, cut the clock and shrink the set until the equation is clean.
How many case math problems should I do before interviews?
Enough tagged sets that your weak operation hits green accuracy twice in a row, then two weeks of mixed tempo. For most candidates I see, that is roughly 150–250 timed items across four weeks, not thousands of unlogged problems.
Should I practice case math with a calculator?
No for live-case prep. The room is pen and rounding. Online assessments sometimes allow a calculator — Bain says its digital assessment is office-specific — so read your invite. Still train without one first so the live round does not feel foreign.
How do I know if I am fast enough at case math?
Use the speed column on the scoring card: about 45 seconds for one-step percent items and 90 seconds for multi-step capacity or contribution. Green accuracy comes first. Fast and wrong is not progress.
What if I freeze before I write the equation?
That is a structure leak, not an arithmetic leak. Pause math sets and rebuild the habit of stating the equation out loud before any multiply. Full-case reps and structure drills fix that faster than more division worksheets.
Sources
- BCG Case Interview Preparation — firm description of case interviews, including quick calculations and reasoning quality. Checked 2026-09-24.
- Bain Digital Assessment — official ~30–40 minute digital assessment and analytical screening before interviews. Checked 2026-09-24.
- Bain Interviewing — consulting path of digital assessment then case interviews. Checked 2026-09-24.
- HBS Employment Data by Industry — Class of 2025 consulting share (21%) and median base ($190k). Checked 2026-09-24.
- BLS Occupational Outlook: Management Analysts — 2024 employment and median pay for the broader analyst/consultant occupation. Checked 2026-09-24.