Future consultants often feel anxious about the math involved in case interviews. It’s easy to get intimidated by thoughts of complex equations and formulas. But don’t stress – with the right preparation, you can master the math side of case interviews.

In this guide, I’ll break down everything you need to know about case interview math. You’ll learn:

• The must-have quantitative skills
• How to perform calculations quickly and accurately
• Common formulas and business metrics
• Expert tips and tricks
• How to avoid mistakes candidates often make

After reading this, you’ll feel confident and prepared to tackle any math that comes up in your case interviews. So let’s get started!

What’s the Deal with Math in Case Interviews?

Many candidates have heard case interviews only involve quick “back of the envelope” math. This isn’t totally accurate. While you won’t face intricate calculus problems, precision and accuracy still matter.

In consulting engagements, even small calculation errors can lead to huge financial consequences for clients. A tiny mistake could mean millions lost in revenue.

Interviewers want to assess your ability to handle numbers precisely and intelligently, even under time pressure. You’ll need to demonstrate you can:

• Quickly understand and break down complex math problems
• Perform accurate calculations in your head
• Spot and correct errors
• Interpret results in a business context

This might sound intimidating. But don’t panic! With practice, you can develop these key skills. The math concepts themselves aren’t too advanced in most cases.

Now let’s dive into the mathematical knowledge you’ll need…

Introduction to “Case Numbers”

In case interviews, you’ll encounter certain types of numbers regularly. I call these “Case Numbers”. They have useful properties that make calculations easier.

There are two main types of Case Numbers:

1. Numbers with Few Significant Digits

These are rounded numbers with just a few non-zero digits. Some examples are:

• $20 million
• 150,000 customers
• $5 billion in revenue

Having only a few significant digits makes these numbers easier to work with in mental math. You don’t need to keep track of a lot of precise figures in your head.

2. “Clean Numbers”

Clean Numbers are a clean fraction times a power of 10. For instance:

• 25,000 = 1⁄4 x 100,000
• 750,000 = 3⁄4 x 1,000,000
• 12.5 million = 1⁄8 x 100 million

The special thing about Clean Numbers is that you can quickly break them down and manipulate them in your head.

With practice, you’ll get very fast at spotting, breaking down, and calculating with these Clean Case Numbers. This skill is incredibly valuable in case interviews.

Let’s look at some examples:

• To multiply 25,000 by 4, I would think:
  25,000 is 1⁄4 of 100,000 So if we multiply it by 4, that’s 1⁄4 of 4 x 100,000 = 100,000 Therefore, 25,000 x 4 = 100,000
• What is 20% of 60 million? 20% of 60 million is the same as 20% of 6 x 10 million Which is 1.2 x 10 million = 12 million

As you can see, breaking Case Numbers into their components makes it much faster to calculate with them mentally.

With practice, you’ll quickly recognize Case Numbers and instinctively break them down. This will give you a major advantage in tackling quantitative problems.

Now let’s look at the essential math skills you’ll need…

Key Math Skills and Techniques

To reliably perform accurate calculations under time pressure, you need to have certain fundamental math skills down cold. Let’s look at each one:

Quick Mental Math Abilities

You need to have strong mental math skills and be able to compute quickly in your head. This includes:

• Addition/Subtraction: Instantly add or subtract numbers
• Multiplication/Division: Mentally multiply or divide numbers
• Percentages: Calculate percentages of amounts
• Estimation: Round numbers and estimate sums

Regular practice with mental math drills will drastically improve your skills over time.

Pro Tip: Try setting a timer and testing yourself on random math problems. The time pressure forces you to calculate quickly.

Fractions, Decimals, and Percentages

Fractions, decimals, and percentages are used constantly in business math. You need to fluidly:

• Convert between fraction, decimal, and percentage formats
• Calculate percentages of amounts
• Express ratios and parts of wholes as fractions and percentages
• Solve problems involving fractions and percentages

Memorize the common percentage conversions, like 25% = 0.25 = 1⁄4. The more second nature these become, the faster you’ll be.

Solving Simple Equations

You’ll need to solve basic linear equations during case interviews. For example:

• Finding break-even points
• Calculating a variable based on other values
• Optimizing profit, revenue, cost, etc.

The equations won’t be complex. But you must feel comfortable setting up and correctly solving one- or two-step equations on the fly.

Compound Interest and Growth

Understanding compound growth rates is essential. You should be able to:

• Calculate compound growth accurately over time
• Estimate how long it takes for a value to double or halve at a given rate
• Determine what growth rate is needed to reach a certain increase

The Rule of 72 is useful here. To estimate doubling time at a growth rate, just divide 72 by the rate.

Statistical Concepts

You may need to calculate or interpret common statistics like:

• Averages – Mean, median, mode
• Weighted averages
• Variance and standard deviation
• Basic probability

Don’t just memorize formulas. Make sure you thoroughly understand what these stats signify and how they’re applied.

With these core skills mastered, you’ll have the quantitative foundation to tackle case interview problems. Now let’s look at some specific business and financial concepts you should know.

Key Business and Financial Concepts

In addition to raw mathematical abilities, you need a good familiarity with business and finance concepts used in consulting. Here are some of the most important ones:

Financial Statements

You should understand key lines on financial statements, like:

• Revenue, gross profit, operating costs on income statements
• Assets, liabilities, equity on balance sheets
• Operating cash flow, capex, investing activity on cash flow statements

Know how to analyze performance and spot trends in the statements.

Breakeven Analysis

Calculate the breakeven point where revenues equal costs. The formula is:

Breakeven Point = Fixed Costs / (Price per Unit – Variable Cost per Unit)

Interpret the significance of results for pricing, profitability, etc.

Return on Investment (ROI)

Know the ROI formula and how to analyze results:

ROI (%) = (Net Profit / Cost of Investment) x 100

A higher ROI indicates a better investment.

Discounting and Net Present Value (NPV)

Understand the present and future value of money, and how to calculate NPV.

NPV estimates the current value of future cash flows. Positive NPV indicates a sound investment.

Economics Basics

Know core economic principles like supply/demand, elasticity, consumer/producer surplus, and competitive advantage.

Accounting Fundamentals

Grasp basics like revenue recognition, cost allocation, working capital, capital expenditure, and more.

Now let’s look at some specific metrics and formulas to remember…

Key Formulas and Metrics

Here are some of the most common financial ratios, metrics, and formulas to memorize:

Profitability Metrics

• Gross Margin – (Revenue – Cost of Goods Sold) / Revenue
• Operating Margin – Operating Income / Revenue
• Net Profit Margin – Net Income / Revenue
• Return on Assets (ROA) – Net Income / Total Assets
• Return on Equity (ROE) – Net Income / Shareholders’ Equity

Liquidity Ratios

• Current Ratio – Current Assets / Current Liabilities
• Quick Ratio – (Cash + Receivables) / Current Liabilities

Solvency/Leverage Ratios

• Debt-to-Equity Ratio – Total Debt / Shareholders’ Equity
• Debt-to-Assets Ratio – Total Debt / Total Assets
• Interest Coverage Ratio – EBIT / Interest Payments

Valuation Metrics

• P/E Ratio – Stock Price per Share / Earnings per Share
• EV/EBITDA – Enterprise Value / Earnings Before Interest, Taxes, Depreciation, Amortization

Make flashcards with these and drill until they’re burned into memory!

Now let’s move on to some key skills for handling math under pressure…

Performing Under Pressure

In case interviews, you’ll have to do math rapidly while explaining your thought process. This can feel stressful! Here are proven strategies to stay cool under pressure:

Tactics for Mental Math Speed

• Memorize tables and common percentages
• Break down problems into simpler steps
• Visualize calculations to process faster
• Utilize Clean Numbers and estimation

Here are some time-saving shortcuts commonly used in case interviews:

Shortcut	Description	Example
Doubling and Halving	Double one factor and halve the other	50 × 16 = 100 × 8 = 800
Distributive Property	Break down complex multiplications	23 × 99 = (23 × 100) – 23 = 2,300 – 23 = 2,277
Rounding and Adjusting	Round to easier numbers, then adjust	48 × 52 ≈ 50 × 50 = 2,500, then subtract 2 × 50 = 2,400
Percentage Chains	Combine percentage changes	10% increase followed by 10% decrease = 0.99, or 1% overall decrease
Fractional Shortcuts	Use fraction relationships for quick divisions	1/3 of 210 = 210 ÷ 3 = 70
Powers of 2	Memorize powers of 2 for quick doubling	2^10 = 1,024 ≈ 1,000 for estimation

With practice, these tactics will help you gain speed and confidence.

Improving Accuracy

• Stop and think before answering – don’t rush!
• Verify your assumptions and inputs
• Check your work, round answers, and recalculate
• Use a structured approach for consistency

This rigorous self-checking prevents careless errors.

Managing Time Effectively

• Quickly estimate time needed per problem
• Tackle easier questions first to build momentum
• Leave time to review your work
• If stuck, make assumptions and come back later

These tips ensure you pace yourself wisely when time is tight.

With technique and experience, you can master the art of delivering solid quantitative analysis while thinking aloud.

Now let’s look at common mistakes to avoid…

Avoiding Common Errors

Here are some of the most frequent errors candidates make with case interview math:

Forgetting to Verify Information

In the rush to start calculating, many neglect to double-check the information provided and clarify assumptions. This often leads to wasted time from incorrect work.

Before starting any problem, pause to verify you have the right information. Explicitly state your assumptions.

Getting Overly Complex

Striving for mathematical elegance can backfire. Interviewers want simple, accurate solutions, not complex equations.

Use the simplest approach that gets the right solution quickly. If stuck in the weeds, take a step back and look for an easier way.

Fumbling Easy Calculations

With nerves and time pressure, candidates often trip up on simple math. Mis-remembering percentages or basic functions can sink you.

If you haven’t done mental math in a while, dedicate time to drill core skills until they’re second nature again. It makes a huge difference.

Forgetting Units and Labels

Omitting units, labels, and proper notation makes solutions messy and ambiguous. Details matter.

Get in the habit of always including units of measure and clearly labeling values in your work. This discipline will pay dividends.

Struggling to Explain Your Thinking

You must discuss your approach aloud. If you struggle to verbalize your process, it raises concerns.

Practice explaining your analysis while going through practice problems. Over time this will feel more natural.

Avoiding these pitfalls will help you demonstrate your quantitative abilities effectively.

Next let’s cover expert tips for acing the math in case interviews…

Pro Tips from Experienced Consultants

After helping hundreds of candidates prepare for case interviews, I’ve picked up some great insider tips:

Use a Structured Framework

Approach each problem using a clear step-by-step framework:

1. Clarify information
2. Make assumptions needed
3. Break down into logical steps
4. Perform calculations
5. Verify results
6. Interpret implications

This disciplined process leads to solid solutions every time.

Learn to Estimate

Develop strong “back of the envelope” math skills through daily practice. You’ll be able to roughly estimate most calculations in your head.

This allows you to sanity-check solutions and catch errors. It also buys you time if you’re stuck on a problem.

Know Your Strengths and Weaknesses

Identify areas you’re less comfortable with and spend more time practicing those skills.

Lean on your strengths in areas you excel at to demonstrate your capabilities.

Overprepare!

You want the math aspects to feel mundane through sheer repetition. The more practice problems you work on, the easier it will feel during actual interviews.

Don’t wait until right before interviews to practice. Start early and make it a regular habit.

These tips have proven successful for candidates time and time again. Now let’s wrap up with some final thoughts…

Conclusion

With the right level of practice and preparation, you can master the quantitative side of case interviews. Approach your preparation with rigor and structure to build flawless skills.

Remember, the math itself is typically not too theoretically complex. The challenges are performing accurately under time pressure while explaining your approach.

By nailing your core math competencies and business knowledge, you’ll shine in the quantitative aspects of case interviews. You got this!

Now you have all the tools needed to tackle any math that comes your way. The more you practice, the more second nature these skills will become. Be diligent in your preparation and you’ll see the results.

You’re on your way to becoming a top-tier consultant! Go into your case interviews with confidence, keep this advice top of mind, and you will succeed.