“Ok, now that you’ve got a structure in place, let’s dive in. Your client operates in a $34B global market, maintains a ~12% market share and earned a 23.2% profit margin last year. How much profit did our client earn last year?”
The above is a prototypical case interview mental math exercise. If you’re preparing for case interviews, you need to be ready to shred problems like that, as well as any infinite permutations of it. Before we jump into discussing the skills necessary to conquer that, let’s refresh our memory on the overall framework of case skills we’re working through.
In our first post in the series, we laid out the key basket of skills that case interviews test you on:
- Analytical skills: problem structuring, charts analysis, mental math
- "Soft" skills: communication, leadership, collaboration, personal drive
Today’s post will be all about sharpening the mental math skills and the charts analysis skills which will let you tackle something like the opening question. Let’s get started.
Mastering mental math
Unless you’re coming from a hard science background or are preternaturally quantitatively gifted (e.g. aced your SAT math section), it’s likely that the mental math component of case interviews will stress you out.
Don’t worry. We’ve got some good news: mental math is a learnable skill! There are two key tips we’ve got that can take you from sweating bullets over mental math to actually enjoying flying through the problems:
- Identify problem categories and techniques for handling them
- Put the magic of compounding to work for you
Identifying categories and appropriate techniques
Like all things in life, mental math becomes much, much easier when you apply a methodical approach to breaking down the problem into bite size chunks. But many candidates never even realize that, they just get stuck at the stage where they despair that their mental math skills are lacking. Don’t be that candidate!
If you’re struggling with mental math, sit down and ask yourself specifically which type of mental math problems are giving you challenges. Is it breakeven problems? Is it multiplying large numbers together and keeping track of all the zeroes? Or compound growth problems? The great news is that whichever type of problem is giving you trouble, there are techniques that will help you master it.
Let’s pick one example: compound growth. Say, you’re asked, “Revenues are currently $300M and growing annually at 3%. What will revenue be in 5 years?” The long, stressful and more error prone way to solve this question is multiply out 3% growth in each year and then repeat it five times. But, that is computationally heavy. A good technique for approaching a question like this is recognizing that consistent compound growth in the single digits can be estimated up front. Thus, 3% * 5 years is 15% growth so 300M + (15% * 300M) is 345M. Thus, we know the answer is a little more than 345M (the exact answer is 347.8M).
Here, a great technique made a tough problem significantly easier. If you consider which problem types challenge you, then you can seek out the right techniques to simplify them!
The magic of compounding
Speaking of compounding, our second tip is to put compounding to work for you. How? By committing to daily practice. Daily investment, even as little as 15 minutes per day, can make you dramatically better.
Let’s say you practice 30 math problems each day for 12 weeks. The first day you get 19 of 30 problems right. Not a great result. Say you practice every day that week and by end of the week you get 20 of 30 right. That’s a roughly 3% improvement that week, or about 0.6% improvement daily. Keep that up for 12 weeks and by the end you’d be getting 27 of 30 questions right… that’s going from 65% right (a D grade) to 90% right (an A grade)!
Analyzing charts like a boss
Ok, let’s talk charts. Quickly glancing at a chart or complicated data display and teasing out the key insights and implications is a skill, just like rattling off a compound growth calculation. Regardless of whether it’s a fairly simple bar chart or a complicated 3-axis bubble chart, there is a systematic way you can approach this as well.
Many candidates treat each chart like a unique problem to be solved anew every time. Don’t do that! Instead, you should stereotype charts. If you understand the different classes of charts and can identify which are which, you can quickly and effectively begin to analyze them. So let’s start by looking at the four types of charts. Ninety-nine percent of all charts you’ll see in interviews (and anywhere) fall into the following four categories:
- Comparison charts (example: a standard bar chart)
- Composition charts (example: a pie chart)
- Relationship charts (example: a scatter plot)
- Distribution charts (example: a histogram)
Let’s do an example. Say, someone gives you a histogram, like the one below which shows the breakdown of purchasers of SUVs by age group.
There are two things that should immediately jump to mind: 1) a histogram is a distribution type of chart and 2) thus, the key insights are likely buried in the aspects of the distribution itself. For example, does it look normally distributed (like a standard bell curve)? Does it look completely random (eg no pattern)? Is it completely flat (eg, the x-axis dimension has no impact).
Applied to chart above, the key insights become obvious after answering our own questions! For this audience, we can state that age certainly has a strong bearing on likelihood to purchase an SUV, and younger people, particularly young adults, are the core market (a 30 year old is 3.5X+ more likely to buy an SUV than a 70 year old).
This is the key: if you identify the type of chart you’re looking at, the key questions you should ask yourself come to mind. Then, as with all things, once you start asking the right questions the answers become obvious.
Today, we covered two key skillsets consulting firms like McKinsey, BCG and Bain care deeply about: mental math and charts analysis. Both can be intimidating, especially if you’re a little rusty. But a structured approach to identifying the specific types of math problems that challenge you and finding the right techniques to solve them will help dramatically. Similarly with charts, keeping a framework in mind of the types of charts will help you ask the right questions and arrive at the right insights. Finally, don’t forget to put compounding to work for you. As little as fifteen minutes a day of targeted skills practice will improve your skills dramatically over time!
Kenton Kivestu is the Founder and CEO of RocketBlocks, an online platform that helps students prepare for case interviews. Prior to RocketBlocks, he worked as a strategy consultant in BCG's San Francisco Office, launched online ad platforms at Google and led the Zynga mobile poker franchise. He has successfully navigated hundreds of case interviews himself and believes that the case interview is an important recruiting tool that helps simulate the on the job experience. He started RocketBlocks to help candidates hone their analytical skills so they can put their best foot forward on interview day. Kenton graduated as an Echols Scholar with distinction from the University of Virginia and holds an MBA from the Tuck School of Business at Dartmouth.
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