Case Interview Math Questions: 15 Fast-Solve Patterns

Case interviews rarely fail because of strategy alone. Many candidates lose momentum on arithmetic they should be able to do in under 10 seconds. The fix is not “do more random math.” The fix is recognizing patterns and applying the same solve sequence every time.

Quick answer: focus on repeatable question families, solve with lightweight mental frameworks, and finish each day with one timed benchmark. If you already run a daily routine, pair this post with the Mental Math for Interviews routine and the Interview Math Hub.

The 15 question patterns interviewers reuse

These are the patterns that appear in consulting, finance, and product cases:

1. Revenue after percentage growth
2. Profit after margin change
3. Blended average across segments
4. Market size from population x penetration x spend
5. Units required to hit target revenue
6. Break-even units from fixed cost and contribution margin
7. Monthly to annual conversion (and reverse)
8. Share-of-market from total and segment size
9. Growth from base and delta
10. CAC payback from CAC and monthly contribution
11. Weighted average price
12. Productivity per rep/team
13. Capacity utilization percentage
14. Retention/churn conversion
15. Sanity-check estimate against rounded assumptions

You can map almost every case arithmetic prompt into one of these patterns.

Fast frameworks for the most common prompts

1) Revenue growth prompt

Prompt: Revenue was $240M, up 18%. What is new revenue?

Fast path:

1. 10% = 24
2. 5% = 12
3. 3% = 7.2
4. 18% = 43.2
5. 240 + 43.2 = 283.2M

If you need a quick estimate first, use 20% = 48, then adjust down.

2) Blended average prompt

Prompt: Segment A is 60% of users at $12 ARPU. Segment B is 40% at $8 ARPU. Blended ARPU?

Fast path:

1. 0.6 x 12 = 7.2
2. 0.4 x 8 = 3.2
3. Total = 10.4

Say the weighted formula out loud so the interviewer follows your logic.

3) Break-even prompt

Prompt: Fixed cost is $1.2M. Price is $60. Variable cost is $35. Break-even units?

Fast path:

1. Contribution per unit = 60 - 35 = 25
2. Break-even units = 1,200,000 / 25 = 48,000 units

If division is slow for you, train this directly with division and averages for interviews.

4) Market sizing prompt

Prompt: Estimate annual coffee shop revenue in a city with 2M adults, 40% weekly buyers, $18 average weekly spend.

Fast path:

1. Active buyers = 2,000,000 x 0.4 = 800,000
2. Weekly spend = 800,000 x 18 = 14,400,000
3. Annual = 14.4M x 52 ≈ 749M

For more setups like this, use market sizing math guide and market sizing examples with answers.

A practical drill workflow (15 minutes)

Use this if you want performance gains in 2-4 weeks.

1. Block A (5 min): percentage/growth prompts only.
2. Block B (5 min): average/division/break-even prompts.
3. Block C (5 min): mixed case-style prompts under time pressure.

Then run a 2-minute benchmark in Timed mode and track:

• Correct answers
• Accuracy
• Avg time/problem
• Which pattern slowed you down

If your score plateaus, switch one block to Focused training for your weakest pattern.

Common mistakes that cost candidates points

• Solving before framing the equation
• Mixing percentage points and percentage change
• Skipping unit checks (monthly vs annual)
• Giving exact numbers when estimation was expected
• Not sanity-checking final magnitude

A quick rule: if the answer sounds implausible, do a 10-second approximation before moving on. Another useful guardrail is to state the unit and timeframe in your final sentence (for example, "annual revenue" or "monthly users"). That one habit catches many avoidable errors before they reach the interviewer.

Related reading

• Mental Math for Interviews: A 10-Minute Daily Routine
• Timed Arithmetic Drills: How to Measure and Improve Speed
• Fast Multiplication Without a Calculator
• Interview Math Practice Hub
• Mental Math Speed Test for Interview Readiness
• Unit Economics Math Guide
• Interview Math Aggregate Insights

FAQ

Next step: run one benchmark now

Open thetamac training, complete a 2-minute mixed benchmark, and write down one pattern that slowed you down. Tomorrow, spend 6 minutes drilling only that pattern. Repeat for a week and compare your score trend on the Leaderboard.