Why Practice Questions Matter
The difference between good and great case interview candidates is practice. These 50 questions cover every major math concept you'll encounter at McKinsey, BCG, Bain, and other top firms.
How to use this guide:
- Set a timer for 60-90 seconds per question
- Write out your work (just like in an interview)
- Check the solution even if you got it right
- Track which topics need more practice
Profitability Questions (1-15)
Q1: Basic Margin Calculation
A company has revenue of $250M and costs of $200M. What is the profit margin?
Solution:
- Profit = $250M - $200M = $50M
- Margin = $50M / $250M = 20%
Q2: Gross Margin
Revenue is $400M, COGS is $280M. Calculate gross margin.
Solution:
- Gross Profit = $400M - $280M = $120M
- Gross Margin = $120M / $400M = 30%
Q3: Revenue from Margin
Operating margin is 15% and operating profit is $45M. What is revenue?
Solution:
- Revenue = $45M / 0.15 = $300M
Q4: Cost Increase Impact
Revenue is $100M with 20% margin. If costs increase by $5M and revenue stays flat, what is the new margin?
Solution:
- Original profit = $20M
- New profit = $20M - $5M = $15M
- New margin = $15M / $100M = 15%
Q5: Price Change Impact
Selling 100K units at $50 each with 40% margin. If price increases 10%, what is the new margin?
Solution:
- New price = $55
- Original cost = $50 × 0.6 = $30
- New margin = ($55 - $30) / $55 = 45.5%
Q6: Blended Margin
Product A: $60M revenue, 25% margin. Product B: $40M revenue, 35% margin. What is blended margin?
Solution:
- Profit A = $15M, Profit B = $14M
- Total = $29M / $100M = 29%
Q7: Volume Change
Price is $100, variable cost $60, fixed costs $2M. Currently selling 100K units. Profit impact if volume drops 20%?
Solution:
- Current contribution = 100K × $40 = $4M, Profit = $2M
- New contribution = 80K × $40 = $3.2M, Profit = $1.2M
- Impact = -$800K (-40%)
Q8: Revenue Mix Shift
Total revenue $200M. Product A (60% of revenue, 20% margin) shifts to 40%. Product B (40% of revenue, 40% margin) becomes 60%. Impact on profit?
Solution:
- Old: 0.6 × 200 × 0.2 + 0.4 × 200 × 0.4 = $24M + $32M = $56M
- New: 0.4 × 200 × 0.2 + 0.6 × 200 × 0.4 = $16M + $48M = $64M
- Improvement = +$8M
Q9: Cost Structure
Revenue $150M. COGS 50%, SG&A 25%, D&A 5%. What is EBITDA margin?
Solution:
- EBITDA = Revenue - COGS - SG&A = $150M × (1 - 0.5 - 0.25)
- EBITDA = $37.5M
- EBITDA Margin = 25%
Q10: Profit per Unit
Revenue $80M from 400K units. Total costs $72M. Profit per unit?
Solution:
- Total profit = $8M
- Profit per unit = $8M / 400K = $20/unit
Q11-15: Quick Fire Profitability
Q11: Revenue $300M, Net margin 8%. Net income? $24M
Q12: COGS is $140M on $200M revenue. Gross margin? 30%
Q13: Operating margin improved from 12% to 15% on $500M revenue. Dollar improvement? $15M
Q14: Variable costs are 70% of revenue. Contribution margin? 30%
Q15: Fixed costs $10M, variable margin 25%. Revenue needed for $5M profit? $60M
Breakeven Questions (16-25)
Q16: Basic Breakeven Units
Fixed costs $500K. Price $100, variable cost $60. Breakeven units?
Solution:
- Contribution margin = $40
- Breakeven = $500K / $40 = 12,500 units
Q17: Breakeven Revenue
Fixed costs $1.2M. Contribution margin 40%. Breakeven revenue?
Solution:
- Breakeven = $1.2M / 0.4 = $3M
Q18: Target Profit
Fixed costs $800K, contribution margin $50/unit. Units to earn $200K profit?
Solution:
- Required contribution = $1M
- Units = $1M / $50 = 20,000 units
Q19: New Product Launch
Launch costs: $2M upfront, $500K annual fixed. Price $200, variable cost $120. Units in Year 1 to recover launch costs and break even on operations?
Solution:
- Contribution = $80/unit
- Total to cover = $2M + $500K = $2.5M
- Units = $2.5M / $80 = 31,250 units
Q20: Price Sensitivity
Current: 50K units at $80, VC $50, FC $1M. If price drops to $70 and volume increases 30%, are we better off?
Solution:
- Current profit = 50K × $30 - $1M = $500K
- New profit = 65K × $20 - $1M = $300K
- No, worse by $200K
Q21-25: Quick Fire Breakeven
Q21: FC $400K, price $80, VC $40. Breakeven? 10,000 units
Q22: Breakeven is 5,000 units at $100. Fixed costs? $500K (assuming reasonable CM)
Q23: Contribution margin 35%, FC $700K. Breakeven revenue? $2M
Q24: Currently at 80% of breakeven volume. FC $600K, CM $30. Current loss? $120K
Q25: Double fixed costs, contribution margin stays same. Impact on breakeven? Doubles
Growth & CAGR Questions (26-35)
Q26: Simple Growth Rate
Revenue Year 1: $80M. Year 2: $96M. Growth rate?
Solution:
- Growth = ($96M - $80M) / $80M = 20%
Q27: CAGR Calculation
Revenue grew from $50M to $80M over 4 years. Approximate CAGR?
Solution:
- Growth multiple = 1.6x
- CAGR ≈ 1.6^(1/4) - 1 ≈ 12%
Q28: Rule of 72
Investment doubles in 6 years. Approximate annual return?
Solution:
- Return = 72 / 6 = 12%
Q29: Future Value
$100M growing at 8% for 5 years. Final value?
Solution:
- $100M × 1.08^5 = $100M × 1.47 = $147M
Q30: Decline Rate
Revenue fell from $200M to $150M over 2 years. Annual decline rate?
Solution:
- 150/200 = 0.75 over 2 years
- √0.75 - 1 = -13.4% annually
Q31-35: Quick Fire Growth
Q31: Market grows 10% annually. Current size $5B. Size in 3 years? $6.65B
Q32: Company A grows 15%, market grows 8%. Relative growth? 7 percentage points faster
Q33: At 7% CAGR, years to double? ~10 years (Rule of 72)
Q34: Revenue was $40M, now $100M after 5 years. CAGR? ~20%
Q35: Inflation 3%, nominal growth 8%. Real growth? ~5%
ROI & Payback Questions (36-45)
Q36: Basic ROI
Investment $500K generates $150K annual profit. 5-year ROI?
Solution:
- Total return = $750K
- ROI = ($750K - $500K) / $500K = 50%
Q37: Payback Period
Investment $1.2M, annual savings $400K. Payback period?
Solution:
- Payback = $1.2M / $400K = 3 years
Q38: Marketing ROI
Campaign cost $200K. Generated $600K revenue with 30% margin. ROI?
Solution:
- Profit = $600K × 0.3 = $180K
- ROI = ($180K - $200K) / $200K = -10% (loss!)
Q39: Cumulative Payback
Investment $800K. Cash flows: Y1 $200K, Y2 $300K, Y3 $400K. Payback?
Solution:
- Y1: $200K cumulative
- Y2: $500K cumulative
- Y3: Need $300K more, get $400K → 0.75 years
- Payback = 2.75 years
Q40: Comparing Projects
Project A: $100K investment, $40K/year for 4 years
Project B: $200K investment, $70K/year for 4 years
Which has better ROI?
Solution:
- A: ROI = ($160K - $100K) / $100K = 60%
- B: ROI = ($280K - $200K) / $200K = 40%
- Project A has better ROI
Q41-45: Quick Fire ROI
Q41: $50K investment, $15K annual return. Simple payback? 3.3 years
Q42: Hurdle rate 15%. Project ROI 18%. Should we proceed? Yes
Q43: Investment triples in 8 years. Approximate annual return? ~15%
Q44: $1M capex, $200K savings/year, 10-year life. Total ROI? 100%
Q45: Two projects same ROI. A: 2-year payback. B: 4-year payback. Which is lower risk? A
Market Sizing Questions (46-50)
Q46: Top-Down Market Size
US population 330M. Estimate annual toothpaste market.
Solution:
- 330M people × 4 tubes/year × $4/tube = $5.3B
Q47: Bottom-Up Revenue
Coffee shop: 200 customers/day, $6 average ticket, 350 days/year. Annual revenue?
Solution:
- 200 × $6 × 350 = $420K
Q48: B2B Market
500 enterprise companies in target segment. Average deal size $200K. Win rate 20%. Realistic TAM capture?
Solution:
- TAM = 500 × $200K = $100M
- Realistic = $100M × 0.2 = $20M
Q49: Per Capita Check
German diaper market estimated at $3B. Germany population 84M. Does this pass sanity check?
Solution:
- Per capita = $36/person/year
- With ~750K births × 2.5 years × $3/day = $2.1B
- Reasonable (includes some adult diapers)
Q50: Growth Projection
Market is $10B growing at 6%. Company has 5% share growing at 12%. Company revenue in 5 years?
Solution:
- Current revenue = $500M
- In 5 years: $500M × 1.12^5 = $881M
What's Next?
You've completed 50 practice questions! Here's how to continue:
- Mental Math Sprint — Build speed under pressure
- Case Math Drills — Interactive business scenarios
- 14-Day Plan — Structured prep schedule
Track your weak areas and keep practicing. Consistency beats cramming.
These quant skills are also valuable for finance interviews. If you're targeting IB, PE, or VC roles alongside consulting, check out Finance Interview Prep for role-specific practice.