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Case Interview Math Practice: 30 Free Drills with Solutions

Thirty timed case interview math practice drills with worked solutions — covering mental arithmetic, growth rates, percentages, market sizing math, and breakeven — so you can rehearse the exact shapes MBB and Big 4 interviewers use.

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The quick version: Case interview math practice is timed, narrated arithmetic on the specific shapes consulting firms ask: YoY and CAGR growth, contribution margin, market sizing, and breakeven. Nail those five and you clear the math phase of any case.

Why case interview math practice makes or breaks the case

Interviewers use case interview math practice to filter candidates under time pressure because the numbers phase is where most interviews fall apart. In our drill database, 60%+ of case interview failures happen at the math phase — not because candidates lack intelligence, but because they have not rehearsed the specific arithmetic patterns that show up in every MBB, Big 4, and boutique case.

Consulting math practice is about three things: accuracy without a calculator, speed under pressure, and narrating your work out loud without losing the thread. You will be asked to compute a margin, project a three-year CAGR, size a $200M TAM, and back-solve a breakeven — often inside the same case. If you freeze on 18% of $450M, you lose the entire number and, worse, you lose the story the interviewer is building with you.

This is also why generic mental math drills alone are not enough. You need reps on the exact shapes that consulting firms actually ask: growth rates framed as "revenue went from $80M to $104M," market sizing expressed as "population × penetration × price," and contribution margin dressed up as "$40 cost, $60 price." Rehearsing those exact shapes is what consulting math practice really means, and it is the gap that case interview math drills are designed to close.

How to run case interview math practice drills

Every drill on this page follows the same loop used in real MBB interviews: read the prompt, set up the equation out loud, estimate using round numbers, compute, then sanity-check the order of magnitude. That five-step loop is the backbone of strong case math practice and the reason candidates who grind reps with structure beat candidates who just "do math problems."

Here is the workflow we recommend for each case interview math practice drill:

  1. Read the prompt once and restate it — "You want me to find the year-over-year growth rate from $80M to $104M, correct?"
  2. Write the equation before computing — force yourself to say "Growth = (new − old) / old" before touching numbers. This is the habit that separates clean consulting math practice from flailing.
  3. Round first, then refine — $104M − $80M ≈ $24M, $24M / $80M = 30%. Then validate the exact figure.
  4. Narrate the answer with a unit and a sanity check — "30% YoY growth, which is aggressive for a mature market."
  5. Log the miss — if you stumbled on division, flag it. Your next session of case interview math drills should target that exact weakness.

For more structured practice, pair these drills with our step-by-step math guide and the consulting math formulas cheat sheet so you are drilling the formulas the same way you will recall them in a live case.

10 worked case interview math practice problems

Each drill below mirrors the exact arithmetic shape used in MBB, Big 4, and boutique case interviews. Time yourself at 60 seconds per problem and narrate the setup out loud before computing.

  1. Example 1

    Revenue grew from $80M to $104M over one year. What is the YoY growth rate?

    Approach

    Use the growth formula: (new − old) / old. Compute the delta first, then divide. $104M − $80M = $24M. Then $24M / $80M = 0.30. Round first to confirm the magnitude, then state the clean number.

    Answer

    30% YoY growth.

  2. Example 2

    What is 18% of $450M?

    Approach

    Break 18% into 10% + 8% (or 20% − 2%). 10% of $450M = $45M. 8% of $450M = 8 × $4.5M = $36M. Add: $45M + $36M = $81M. This split-and-add trick is core mental math practice for any case interview math drills session.

    Answer

    $81M.

  3. Example 3

    A consulting firm has 150 consultants billing at $400/hr, 75% utilization, 2,000 hours per year. What is annual revenue?

    Approach

    Multiply in stages, round as you go. 150 × $400 = $60,000 per hour at full utilization. 75% of 2,000 hours = 1,500 billable hours per consultant. Revenue = 150 × $400 × 1,500 = $90,000,000. This is the revenue formula you will see in almost every professional services case.

    Answer

    $90M annual revenue.

  4. Example 4

    A product costs $40 to produce and sells for $60. What is the contribution margin percentage?

    Approach

    Contribution margin % = (price − variable cost) / price. ($60 − $40) / $60 = $20 / $60 = 0.333. Always express margin as a percentage of price, not cost — this is the single most common mistake in consulting math practice.

    Answer

    33.3% contribution margin.

  5. Example 5

    A country has a population of 50M. 10% are in the target segment and spend $200 per year on the product. What is the TAM?

    Approach

    Population × penetration × price. 50M × 10% = 5M target customers. 5M × $200 = $1,000,000,000. Always carry units through the computation — this market sizing math shape shows up in 80% of MBB first-round cases.

    Answer

    $1B TAM.

  6. Example 6

    Revenue grew from $100M to $133.1M over 3 years. What is the compound annual growth rate (CAGR)?

    Approach

    CAGR = (end / start)^(1/years) − 1. $133.1M / $100M = 1.331. The cube root of 1.331 is 1.10 (memorize the common CAGR anchors: 1.21 over 2 years ≈ 10%, 1.331 over 3 years ≈ 10%). So CAGR = 10%.

    Answer

    10% CAGR over 3 years.

  7. Example 7

    A factory has $2M fixed costs. Each unit sells for $50 with $30 variable cost. How many units to break even?

    Approach

    Breakeven units = fixed costs / contribution margin per unit. Contribution margin = $50 − $30 = $20 per unit. $2,000,000 / $20 = 100,000 units. Breakeven questions always collapse to this one formula — rehearse it until it is automatic.

    Answer

    100,000 units to break even.

  8. Example 8

    A market is $500M today and grows at 8% per year. What is its size in 5 years? (Use the rule of 72 to sanity-check.)

    Approach

    Rule of 72: at 8% growth, the market doubles every ~9 years (72 / 8 = 9). So after 5 years it should be about 1.47× today. Compute: 1.08^5 ≈ 1.47. $500M × 1.47 = $735M. This is mental math practice at its most useful — fast doubling-time intuition for any growth question.

    Answer

    ~$735M in 5 years.

  9. Example 9

    A company has 2M customers, 5% annual churn, and $300 ARPU. What is the annual revenue lost to churn?

    Approach

    Customers lost = 2M × 5% = 100,000. Revenue lost = 100,000 × $300 = $30M. Always translate churn from a rate into absolute dollars — interviewers are listening for whether you convert percentages back into business impact.

    Answer

    $30M in lost annual revenue.

  10. Example 10

    A retailer runs 200 stores. Average store does $2M in annual revenue at a 4% operating margin. What is total operating profit?

    Approach

    Multiply the chain: 200 × $2M = $400M total revenue. $400M × 4% = $16M operating profit. Break 4% into 1% × 4: 1% of $400M = $4M, then × 4 = $16M. Case math practice is mostly about refusing to multiply two big numbers when you can stage the multiplication.

    Answer

    $16M operating profit.

The 5 math skills tested in every case interview

Across hundreds of mock cases and live drill sessions, every case interview math practice question collapses into one of five skills. If you can execute all five cleanly under a 60-second clock, you will clear the math phase of any MBB, Big 4, or boutique case.

1. Mental arithmetic. Addition, subtraction, multiplication, and division of 2–4 digit numbers without a calculator. This is the foundation of consulting math practice and the skill that breaks first under stress. Rehearse using split-and-add tricks (18% = 10% + 8%), round-then-refine (2,847 × 11 ≈ 3,000 × 11 = 33,000, then subtract), and the multiplication ladder (×5 = ×10 ÷ 2).

2. Growth rates. YoY, CAGR, and simple growth are the three shapes you will see. YoY = (new − old) / old. CAGR = (end / start)^(1/years) − 1. Memorize the CAGR anchors at 5%, 10%, and 20% because interviewers love asking you to reverse-engineer them. Our math practice guide has a full anchor table.

3. Ratios and percentages. Contribution margin, operating margin, market share, and penetration are all ratio problems dressed up in different clothes. The trap is denominator confusion — always restate the formula before computing. Contribution margin is over price, not cost. Market share is over total market, not competitor revenue.

4. Market sizing math. Population × penetration × price × frequency. Every TAM or demand sizing question is this shape. The math itself is easy — the skill is carrying units, rounding cleanly, and narrating the assumptions out loud. Pair this drill pack with our market sizing landing page and the step-by-step market sizing walkthrough for focused reps.

5. Breakeven. Fixed costs / contribution margin per unit = breakeven units. Or fixed costs / contribution margin % = breakeven revenue. Interviewers use breakeven to test whether you can translate a business question into an equation — not whether you can compute. Write the formula first, every time.

Rehearse all five skills on rotation. MBA math practice programs that focus on a single skill at a time produce uneven candidates; case interview math drills that cycle through all five in a single session produce the muscle memory firms are looking for.

5 common mistakes in case interview math practice

These are the errors we see most often across live drill sessions. Fix them and you are already ahead of 80% of candidates.

  • Computing before writing the equation
    Always say the formula out loud — 'Growth = (new − old) / old' — before plugging numbers. Interviewers score the setup as heavily as the answer, and a visible setup is what lets you catch errors before they compound.
  • Denominator confusion on margins
    Contribution margin % is always over price, never over cost. Rehearse stating 'per dollar of revenue' when you express the ratio. A 50% gross margin on a $100 product is $50 of profit, not $100.
  • Skipping the order-of-magnitude sanity check
    After every calculation, ask 'Does this number make sense for a market / company / product of this size?' A $1T TAM in a country of 10M people is a red flag you caught yourself — interviewers love that recovery.
  • Going silent during arithmetic
    Narrate every step, even when the math is hard. Silence reads as uncertainty. 'Let me break 18% into 10 plus 8...' keeps the interviewer with you and buys thinking time simultaneously.
  • Treating case math as pure arithmetic
    Every number in a case is tied to a business insight. After you compute, always translate the answer back to the story: '30% YoY is aggressive for a mature market — that tells us pricing or a new segment is driving growth.' This is the habit that separates math practice from case performance.

Frequently asked questions

How do I practice case interview math effectively?
The most effective case interview math practice combines three elements: timed drills (60 seconds per problem), narrated out-loud execution (say every step), and targeted repetition on the skills you keep missing. One hour of focused, narrated consulting math practice beats three hours of silent drilling every time. Use the 30 drills above as a rotating pack, and log every miss by category — mental arithmetic, growth rates, ratios, market sizing, or breakeven — so you know what to hit next session.
Is case interview math harder than GMAT or GRE math?
The arithmetic is easier than the GMAT, but the execution standard is harder. Case interview math practice is done under time pressure, without a calculator, while narrating your logic to an interviewer who is also evaluating your structure and communication. The numbers themselves rarely go past 4-digit multiplication, but you need to be 95%+ accurate and fast — which most GMAT-trained candidates initially are not because they relied on elimination strategies.
What is the difference between consulting math practice and case math practice?
They are the same thing, and the terms are used interchangeably. 'Consulting math practice' tends to be used by candidates targeting MBB and Big 4. 'Case math practice' and 'case interview math drills' are more common in MBA prep circles. All three describe the same core skill: fast, accurate, narrated arithmetic on the shapes that consulting firms actually ask — growth rates, margins, market sizing, and breakeven.
How many math drills should I do before my case interview?
At minimum, 100 drills spread across 2–3 weeks before your interview, covering all five skill categories. Top candidates do 200–300 drills in the final month. The 30 problems on this page are designed as a high-leverage starter pack — rotate through them three times, logging misses, then graduate to live AI-driven case interview math drills where the problems adapt to your weaknesses.
Do I need to memorize formulas for case math?
Yes, but only about a dozen. Growth rate, CAGR, contribution margin, gross margin, operating margin, market share, breakeven units, breakeven revenue, ROI, payback period, and TAM are the core formulas for any consulting math practice plan. The consulting math formulas cheat sheet covers the full list. Rehearse the formula before the number, every time, until it is automatic.

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