Formula for growth

When it comes to case interviews, data interpretation is a crucial skill that sets top candidates apart. Whether you're analyzing market trends, customer segments, or financial figures, your ability to quickly understand and communicate data-driven insights can make or break your performance. In this guide, we'll break down the process into three simple steps to help you excel in reading and interpreting charts and data during your interviews. Two Types of Data Interpretation in the Recruiting ProcessWhen preparing for your career in consulting, you'll encounter two primary scenarios where data interpretation comes into play:Solving specific tests (like the McKinsey Solve Game): This requires precise calculations and often involves mental math.Analyzing and communicating business insights: This is the core of case interviews, where you’ll need to interpret data, connect it to the case context, and use it to drive the discussion.This article will focus on the second aspect: how to analyze and communicate business insights in a case interview. If you're interested in improving your skills for specific tests, be sure to check out our resources on the McKinsey Solve Game and BCG Online Case.💡 Bonus Tip: The sooner you develop excellent data interpretation skills, the better. Check out your skill level now by taking our quiz on Graph and Chart Reading! A Three-Step Guide to Reading Charts and Data in Case InterviewsIn a case interview, you won’t be solving straightforward math problems; instead, you’ll be tasked with interpreting data to uncover business insights. Data in various forms is likely to make an appearance in many different types of cases. For example, when you ask for market, customer, or cost information while analyzing the case, the interviewer may provide you with a slide that has a few graphs detailing the various segments of the target market and several numbers (revenue, growth, etc.) pertaining to the segments. To work with this data effectively, you can follow a simple three-step approach: analyze, contextualize, and interpret. Step 1: Analyze – Understanding the DataWhen you're presented with data during a case interview, the first step is to analyze it thoroughly. There are three forms in which the data can be presented to you:Only numerical data is in a tabular form.Bar or pie charts with markings on the axes indicating units and reference data points.A mixture of tabular and graphic representations of data.Start by examining the exhibit. Reading the title will give you an initial understanding of what the data represents. Pay close attention to the axes, units, and labels, as these elements clarify what's being measured. For instance, if you're analyzing market size, quickly identify the most relevant numbers such as revenue and growth rates and use them to work through your analysis.Example: Suppose you're working on a case for a boot manufacturer that produces two types of boots: work boots and casual boots (👉 here you can find the whole case). You're tasked with planning a strategy in response to a competitor launching a new product. To understand the market, you ask the interviewer for market size data, and you're presented with the following exhibit: Take the following steps to analyze this data:Keep the question in mind: Always remember the question you asked the interviewer when they handed you the exhibit. Your primary job is to answer that question. In this case, you're focused on determining the market size – a figure in euros. Therefore, you must assimilate all the customer segmentation, product, and pricing data into the total market size.Study the exhibit: Begin by reading the title of the exhibit and then studying the axes and units of the data. This will tell you what the data is about. In this case, the exhibit is a mixed chart with both numerical and graphical representations. The first part shows buying propensity (the percentage of the population that bought boots last year). The data is presented as a percentage for different customer segments. Additionally, you have the average price paid and total population for each segment.Work the math: Figure out the most efficient approach to get to the final result, and do the calculations. If all the required data isn’t present, don’t hesitate to ask for it.For instance:Total revenue from all customers would equal the market size.Total revenue = Number of boots bought * Price per pairNumber of boots bought = Number of buyers * Boots bought per buyerNumber of buyers = (Total Population) * (% of the population buying boots)Now, do we have all the information required to calculate the revenue? Not quite yet. You need to know the number of boots bought per capita by each consumer segment. Quickly explain your approach to the interviewer and ask for the required information. Suppose the interviewer asks you to assume that every customer bought just one pair of boots in the last year.Now, you have all the information needed to calculate the market size for the total boots category. However, you cannot calculate the size of the work boots versus casual boots market separately since you only know the overall average price and not the category average for each. While these individual prices for the categories can technically be calculated using simultaneous equations, it’s overkill for a case interview, so you should ask the interviewer for this information to calculate the different segments.After completing the calculations, let's make some straightforward observations. Blue-collar workers buy more work boots than casual boots. Since they’re paying more than others on average, it could imply that work boots are more expensive than casual boots. Additionally, the work boot category is significantly larger than the casual boot category. Step 2: Contextualize – Connecting Data to the CaseAfter analyzing the data, the next step is to contextualize it within the broader case. This means linking the numbers back to the overall business problem you're trying to solve. For instance, relating the data to the case objective is crucial. If the case is about entering a new market, consider how the market size data influences your decision-making process. A large, growing market might suggest a strong opportunity, but you must also consider factors like competitive intensity and customer needs.By contextualizing the data, you ensure that your analysis supports a strategic recommendation. This means not just identifying what the data says, but also why it matters to the client’s goals. For instance, if the data reveals that a specific customer segment is both sizable and underserved, your strategy might focus on targeting this segment with a tailored product offering. This approach not only answers the immediate case question but also aligns your recommendation with the broader business objectives of growth and market penetration.In our boot manufacturer example, if you’ve determined that the work boot segment is larger and more profitable, and that it’s primarily driven by blue-collar workers, this information will guide your strategy. You might hypothesize that focusing on the work boot segment could be the most effective strategy for capturing market share from the new competitor, especially if you identify opportunities to differentiate your products or address unmet needs in this segment as a competitive response. Step 3: Interpret – Drawing Insights and Driving the DiscussionThe final and most important step is synthesizing all the analysis and business reasoning that you just completed and presenting it to the interviewer effectively. Communicate your insights clearly and concisely, ensuring that your conclusions are backed by the data. This approach not only demonstrates your analytical skills but also shows that you can use data to make strategic business decisions.In our boot manufacturing example, this could look as follows:"Our strategy should focus on further capturing the blue-collar worker segment, which is the most profitable for our work boots category. This segment accounts for [X]% of our total revenue, with an average price of [Y] euros per pair—higher than other segments. Given its significant contribution and [Z]% growth over the last [A] years, we should enhance product features such as durability and safety to meet their specific needs. Additionally, targeted marketing and partnerships with industrial employers or safety equipment suppliers could expand our reach and strengthen our position in this key market."Based on the Pyramid Principle of effective communication, the recommendation is communicated upfront, followed by the supporting data and rationale. Moreover, the hypothesis is clearly tied to specific data points, making the reasoning behind the strategy transparent and grounded in the analysis. Extra Tips to Work with Data and Charts in Case InterviewsMastering data interpretation requires more than just understanding the process during the interview; it’s also about thorough preparation. The following tips will help you sharpen your skills:1. Practice with real case studies: One of the most effective ways to prepare is by working through real case studies that include data-heavy exhibits. This will not only help you get familiar with the types of data presentations you might encounter, but it will also improve your ability to quickly extract relevant insights under time pressure. As you practice, focus on interpreting different types of charts, such as bar charts, line graphs, and pie charts, as well as numerical tables. The following cases can be a good starting point:👉 Company Case by Deloitte: Footloose 👉 Company Case by tkMC: Portfolio optimization of a holding company👉 Expert Case by Luca: Espresso, Whatelse? To really get comfortable interpreting data under pressure, simulate the interview environment. Set a timer, review a case with a data exhibit, and practice explaining your analysis and conclusions out loud. The best way to do this is by conducting mock interviews with peers. Check out our Meeting Board to find like-minded candidates to practice with. This will not only improve your speed and accuracy but also help you build the confidence needed to communicate your findings effectively in a real interview.2. Enhance your mental math skills: Although many cases don’t require complex calculations, being quick with mental math can significantly speed up your analysis. Work on improving your mental arithmetic, especially in areas like percentages, ratios, and basic multiplication/division. Our Mental Math Tool can get your math skills up to speed.3. Familiarize yourself with common data representations: Charts and graphs come in many forms, and each has its nuances. Spend time learning about different types of data representations – such as histograms, scatter plots, and stacked bar charts – and understand when and why they are used. This familiarity will allow you to quickly interpret the data during your interviews, as you’ll already know what to look for and how to analyze it. Final Thoughts About Charts and Data in Case InterviewBy following our three-step guide – analyzing the data, contextualizing it within the case, and interpreting it to drive the discussion – and integrating our preparation tips into your study routine, you’ll be well-equipped to tackle any data-heavy case interview with confidence. Remember, the key to success in these interviews isn’t just about crunching numbers; it’s about turning those numbers into actionable business insights. Keep practicing, stay curious, and approach each case with a strategic mindset.

Math plays a big role in case interviews because it helps you solve business problems logically and in a structured way. It’s not about applying complex formulas; it’s about working quickly with numbers and finding practical solutions. Since you won’t have a calculator and can only use pen and paper, knowing effective calculation methods is key. These skills show off your analytical mindset and can make you stand out from other candidates. Why Mental Math is a Big PlusIn case interviews, being able to handle basic calculations in your head is a huge advantage. It saves time and makes you appear more flexible and confident. It’s not about avoiding writing things down entirely, it’s rather about quickly grasping the results. The goal is to get a fast overview and deliver precise answers. Imagine calculating revenue and profit for multiple products – if you can confidently do these calculations in your head, you’re already a step ahead. Working with Rounded NumbersIn case interviews, you’ll often see “rounded” numbers like 300,000 or 4,000,000. Working with large numbers can feel intimidating, but a few simple tricks can make it much easier.💡 Quick Trick: Cutting ZerosLet’s say you’re calculating the revenue for a product that a company sells at $32 per unit, with 25,000 units sold annually. The calculation is 32 × 25,000. Instead of writing all those zeros, break it into simpler steps:Calculate 32 × 25 first, which is easier than 32 × 25,000.Then, just add the three zeros from “25,000” to the result.To quickly solve 32 × 25, you can think of 25 as ¼ × 100:32 × ¼ = 88 × 100 = 800So, 32 × 25 is 800, making 32 × 25,000 equal to 800,000. This method saves time and reduces the chance of misplacing zeros. Adding and Subtracting with UnitsLarge numbers, like 250 million or 300 million, might seem challenging at first glance. A useful technique is to work with units like thousands (K), millions (M), billions (B), and trillions (T). This simplifies addition or subtraction because you don’t have to write out or imagine all the zeros.💡 Quick Trick: Adding Large NumbersSuppose you need to add 250 million, 300 million, and 150 million. Instead of writing each number fully, just add the leading numbers and keep the unit:250 + 300 + 150 = 700, then add the “million” unit."The result is 700 million. This approach is quicker and reduces errors since you’re focusing only on the main numbers, not all the extra zeros. Multiplication and “Clean Numbers”Multiplication is common in case interviews, and many numbers used are “clean numbers”, meaning they have helpful properties that make calculations easier. For example, 25 is a “clean” number because it’s ¼ × 100, which simplifies large multiplications.💡 Quick Trick #1: Fast-Math Multiplication:The Fast-Math Method is a technique for simplifying complex multiplications by breaking them into easier steps. It’s based on the idea that you can halve one number and double the other without changing the result, thanks to the commutative property of multiplication. This keeps the final product the same but often makes the math easier. Here’s an example:Original calculation: 160 × 350Halve 160: 160 ÷ 2 = 80Double 350: 350 × 2 = 700Multiply the results: 80 × 700 = 56,000The result is the same as 160 × 350 but without lengthy calculations. This method is especially handy in case interviews, allowing for quick, error-free calculations.💡 Quick Trick #2: Reordering Multiplication Factors:Another helpful technique is rearranging terms to make the multiplication easier. Imagine you need to calculate 125 × 2.5 × 4. You can rearrange like this:Start with 125 × 4 = 500.Then, 500 × 2.5 = 1,250.The answer is 1,250. Reordering simplifies the calculation. You could also do 2.5 × 4 = 10, then 125 × 10 = 1,250. This flexibility lets you choose the easiest order for each case. Quick Calculations for Percentage GrowthLet’s say a company grows 4% per year. Calculating this over multiple years can often be simplified by ignoring compound interest and estimating growth. This is especially helpful for shorter time periods and moderate growth rates.Example: Estimating Percentage GrowthIf a company’s revenue is $400 million and it grows at 4% annually for six years, you can estimate the growth like this: 4% × 6 = 24%, which is roughly one-quarter. So the revenue grows by about 25%, or around $100 million, bringing it to about $500 million after six years. This method gives a quick estimate for growth impact over several years. The Net Present Value (NPV) MethodThe Net Present Value (NPV) method is a common approach to calculate the current value of a future investment. It helps determine today’s value of expected cash flows by discounting future payments. A positive NPV indicates a worthwhile investment, as future returns exceed the initial cost.💡 Quick Trick: Rule of 72The “Rule of 72” is a tool for estimating the doubling time of an investment—how long it’ll take to double in value. The Rule of 72 uses the exponential growth formula and can be applied when a rate of return (or growth rate) is known.Simply divide 72 by the annual interest rate (in percent) to estimate the doubling time. For example, if the growth rate is 6% annually, the investment doubles in about 12 years (72 ÷ 6 = 12).This quick estimation helps estimate the future value of an investment without needing to apply the exact NPV formula. Since it’s an approximation, it’s great for quick decisions or rough estimates but less suited for precise calculations.Example: NPV of a Real Estate ProjectA real estate company is considering a project that will sell apartments for $250 million in six years. What’s the current value of this investment if they expect a 12% return annually? Using the Rule of 72, an investment with a 12% growth rate doubles in about six years (72 ÷ 12 = 6). So, today’s value is roughly half the future value, or $125 million. This means the company should invest no more than $125 million to achieve a 12% return. ConclusionMath and quick calculations are essential in case interviews to help you stand out from other candidates. The methods and examples here allow you to tackle common calculations efficiently and accurately. From working with rounded numbers to using the Fast-Math Method, these techniques make you faster and more confident with numbers. Practice these methods before your interview to be flexible and confident, showcasing your math skills effectively.👉 Elevate your math skills to the next level by practicing with our Mental Math Tool!