Case Interview Math Drills: Practice Questions with Answers

Revenue, profit, and margin drills

1. Revenue decline

A retailer sells 2 million units at $40. Volume falls 10% and price rises 5%. New revenue is 1.8 million units times $42, or $75.6 million. The business loses $4.4 million versus the original $80 million.

2. Profit margin

A product has $120 million revenue and $78 million total cost. Profit is $42 million and margin is 35%. In a case, explain whether that margin is improving, declining, or attractive versus alternatives.

3. Breakeven

A new service requires $6 million in fixed cost and earns $30 contribution per customer. Breakeven is 200,000 customers. The next question is whether the market and channel can realistically deliver that volume.

Growth and market sizing drills

4. Market size

There are 40 million target households, 25% buy the product, and each spends $300 per year. Market size is 40 million x 25% x $300 = $3 billion annually. The takeaway is whether that profit pool is large enough for the client to enter.

5. Three-year growth

A business grows from $100 million to $133 million in three years. Because 1.10 cubed is about 1.33, the rough CAGR is 10%. Say the shortcut out loud so the interviewer can follow your rounding.

6. First-year sales

The addressable market is $2 billion and the client expects 3% penetration in year one. First-year sales are $60 million. The next question is whether distribution and awareness can support that share.

How to say the math out loud

Before calculating, say the equation. During calculation, keep units attached to every number. After the answer, add the implication: "That means the client needs roughly 200,000 customers to break even, so the launch only works if we believe the acquisition plan can reach that scale."

Pricing, mix, and operations drills

7. Price increase

A company sells 5 million units at $20. It raises price 8% and volume falls 3%. New price is $21.60 and new volume is 4.85 million, so revenue is about $104.8 million versus $100 million before. Revenue rises by about $4.8 million.

8. Segment profit pool

Segment A has $500 million revenue at 10% margin, or $50 million profit. Segment B has $300 million revenue at 25% margin, or $75 million profit. Even though Segment A is larger, Segment B has the better profit pool.

9. Weighted average margin

A company has 70% of revenue at 20% margin and 30% at 5% margin. Weighted margin is 70% x 20% plus 30% x 5% = 15.5%. The business implication is that mix shift toward the low-margin segment could hurt profitability.

10. Capacity utilization

A plant can make 1 million units per year and currently produces 750,000. Utilization is 75%. If demand rises above 1 million, the client needs overtime, outsourcing, or new capacity.

11. Cost reduction

A client has $240 million in annual cost. Procurement is 35% of cost, and a sourcing initiative can reduce procurement spend by 12%. Savings are $240 million x 35% x 12% = $10.1 million. Tie the answer to whether the savings are material.

12. Payback period

A project costs $18 million upfront and generates $6 million in annual profit improvement. Payback is three years. The recommendation depends on whether a three-year payback fits the client's risk tolerance and capital priorities.

Common math mistakes

The biggest case math errors are rarely advanced formulas. Candidates lose points by dropping units, mixing annual and monthly numbers, overusing exact arithmetic, or forgetting to interpret the result. Clean setup is more important than speed at the start.

If you are searching for case interview math practice PDF resources, use these drills as a reusable checklist: revenue, profit, margin, breakeven, growth, weighted average, market sizing, and exhibit interpretation.

Practice in the trial lab Consulting practice guide