Practice makes perfect. Here are 30 realistic case math questions organized by topic. Try each one, then check the solution.
How to Use This Problem Bank
- Time yourself: Aim for 60-90 seconds per question
- Show your work: Write out calculations as you would in an interview
- Check the answer: Review the solution even if correct—there may be a faster approach
- Track weak areas: Note which topics need more practice
Profitability Questions (1-10)
Q1. A company has revenue of $200M and a 35% gross margin. What's the gross profit?
Solution: $200M × 0.35 = $70M
Q2. Operating income is $25M on revenue of $150M. What's the operating margin?
Solution: $25M / $150M = 16.7% ≈ 17%
Q3. A retailer sells 50,000 units at $40 each with variable costs of $28 per unit. Fixed costs are $400,000. What's the total profit?
Solution:
- Revenue: 50,000 × $40 = $2M
- Variable costs: 50,000 × $28 = $1.4M
- Contribution: $2M - $1.4M = $600K
- Profit: $600K - $400K = $200K
Q4. If gross margin drops from 45% to 40% on $100M revenue, how much profit is lost?
Solution: 5 percentage points × $100M = $5M
Q5. A product has 60% gross margin. Price is $50. What's the COGS per unit?
Solution: COGS = Price × (1 - Margin) = $50 × 0.40 = $20
Q6. Revenue increased 20% and costs increased 25%. Original profit was $10M on $100M revenue ($90M costs). What's the new profit?
Solution:
- New revenue: $120M
- New costs: $90M × 1.25 = $112.5M
- New profit: $120M - $112.5M = $7.5M
Q7. A business has three product lines with margins of 20%, 35%, and 50% on revenues of $40M, $30M, and $30M respectively. What's the blended margin?
Solution:
- Weighted profit: $8M + $10.5M + $15M = $33.5M
- Total revenue: $100M
- Blended margin: $33.5M / $100M = 33.5%
Q8. If SG&A is 18% of revenue and revenue is $85M, what's the SG&A expense?
Solution: $85M × 0.18 = $15.3M
Q9. A company wants to improve profit by $5M. Operating margin is 10%. How much additional revenue is needed (assuming same margin)?
Solution: $5M / 0.10 = $50M
Q10. Net profit is $12M. Tax rate is 25%. What's pre-tax profit?
Solution: Pre-tax = $12M / (1 - 0.25) = $12M / 0.75 = $16M
Breakeven Questions (11-18)
Q11. Fixed costs are $600K. Price is $100, variable cost is $60. What's breakeven in units?
Solution: $600K / ($100 - $60) = $600K / $40 = 15,000 units
Q12. Using Q11 data, what's breakeven revenue?
Solution: 15,000 × $100 = $1.5M
Q13. A SaaS company has monthly fixed costs of $200K. Subscription is $50/month with $10 variable cost. How many subscribers to breakeven?
Solution: $200K / ($50 - $10) = $200K / $40 = 5,000 subscribers
Q14. If fixed costs increase by 20%, how does breakeven change?
Solution: Breakeven increases by 20%. If it was 15,000 units, now it's 18,000 units
Q15. Contribution margin is 40%. Fixed costs are $800K. What revenue is needed to breakeven?
Solution: $800K / 0.40 = $2M
Q16. A company needs to sell 10,000 units to breakeven. Price is $75. Fixed costs are $300K. What's the variable cost per unit?
Solution:
- Breakeven: FC / (P - VC) = 10,000
- $300K / (75 - VC) = 10,000
- 75 - VC = 30
- VC = $45
Q17. Current sales are 20,000 units. Breakeven is 12,000 units. What's the margin of safety in percentage?
Solution: (20,000 - 12,000) / 20,000 = 8,000 / 20,000 = 40%
Q18. A company wants to make $100K profit. Fixed costs are $400K, contribution margin is $25/unit. How many units must they sell?
Solution: ($400K + $100K) / $25 = $500K / $25 = 20,000 units
Growth & CAGR Questions (19-24)
Q19. Revenue grew from $50M to $60M. What's the growth rate?
Solution: ($60M - $50M) / $50M = $10M / $50M = 20%
Q20. A company growing at 15% annually has $100M revenue today. What's revenue in 3 years?
Solution: $100M × 1.15³ = $100M × 1.52 ≈ $152M
Q21. Revenue went from $80M to $125M over 4 years. What's the approximate CAGR?
Solution:
- Multiple: 125/80 = 1.56
- CAGR ≈ 1.56^(1/4) - 1 ≈ 12%
- Verify: 80 × 1.12⁴ ≈ 126M ✓
- ~12%
Q22. At 10% growth, how many years to double revenue?
Solution: Rule of 72: 72/10 = ~7 years
Q23. Market is growing at 8%. Company A is growing at 12%. What's Company A's growth relative to market?
Solution: 12% - 8% = 4 percentage points above market, or 12/8 = 1.5x market growth
Q24. If something triples in 12 years, what's the approximate CAGR?
Solution:
- 3^(1/12) - 1 ≈ 9.6%
- Quick check: Rule of 72 → doubles in 7.2 years at 10%. Triple in ~12 years is close.
- ~10%
ROI & Payback Questions (25-30)
Q25. Investment: $2M. Annual profit: $500K. What's the simple payback period?
Solution: $2M / $500K = 4 years
Q26. A $1M marketing campaign generates $1.5M in revenue with 30% margin. What's the ROI?
Solution:
- Profit: $1.5M × 0.30 = $450K
- ROI: ($450K - $1M) / $1M = -55%
- -55% (loss)
Q27. Project costs $5M and generates profits of $1M, $1.5M, $2M, $2M in years 1-4. What's the payback period?
Solution:
- Cumulative: $1M, $2.5M, $4.5M, $6.5M
- Crosses $5M between year 3 and 4
- Year 3: $4.5M. Need $0.5M more.
- Year 4 generates $2M. $0.5M / $2M = 0.25 year
- Payback: 3.25 years
Q28. Two investments: A has 20% ROI, B has 30% ROI. A costs $1M, B costs $3M. Which generates more absolute return?
Solution:
- A return: $1M × 20% = $200K
- B return: $3M × 30% = $900K
- B generates $700K more
Q29. An investment has 3-year payback. If the asset lasts 10 years with constant returns, what's the approximate total ROI?
Solution:
- Annual return: Investment/3
- 10-year return: Investment × (10/3) = 3.33× investment
- ROI: (3.33 - 1) / 1 = 233%
Q30. Company hurdle rate is 12%. Project A: 15% ROI, 4-year life. Project B: 10% ROI, 8-year life. Which should they choose?
Solution:
- A exceeds hurdle (15% > 12%) ✓
- B below hurdle (10% < 12%) ✗
- Choose A (B doesn't meet minimum return)
Next Steps
These questions mirror the math you'll face at McKinsey, BCG, Bain, and other top firms. For more practice:
- Mental Math Sprint — Build calculation speed
- Case Math Drills — Interactive practice with explanations
- 14-Day Plan — Structured preparation
Practice daily. Track progress. Ace the interview.