*(This article is part 3 of the series “The 5 ways to be MECE”, to go back to part 2, click here. To go back to part 1, click here)*

What if I told you basic high school algebra is one of the keys to always have a custom MECE structure for just about any problem? Crazy, right?

That’s exactly what Algebraic structures are: applied algebra. You can structure any numerical problem by breaking it down into an equation with real variables. Not x’s and y’s, but “revenues per customer” and “hiring costs”. Doing this is vital for consulting work as well as case interviews.

If you’re not fluent at this, you’re gonna have to wait until the stars align before you get your job offer. No wonder consulting firms use estimation cases so much (yes, even MBB). That’s the quickest way to test this skill. But many candidates never realize they can use this to structure other types of problems as well. And when they do, they’re suddenly not relying on any stars anymore.

Most organizations use numbers to measure their performance, and these metrics are often tied to the performance of the executives who run these organizations. Many case interviews are about an executive trying to improve a particular metric. Profits, Revenues, Costs, Market share, Customer evasion rates, Production efficiency, Literacy rate, you name it. Each of these could be the goal of an executive.

If your case revolves around a specific metric, you can break it down into the algebraic components. Profits would be either “Revenues – Costs” or “Revenues * % Margin”. Customer evasion = “Customers we ourselves stopped serving + customers who moved to competition + customers who stopped using this type of service”. Hiring costs = “# of people hired * cost per hire”.

Algebraic structures guarantee MECEness because a formula *has* to yield the target metric. It’s how math works. You can check for MECE using simple high school-level dimensional analysis. Another pro of this technique is that you can quantify how much effect comes from which source. If hiring costs have gone up is 100% of the effect coming from more hires? Or did we just hired 20% more people and our cost per hire has soared abruptly?

### Algebra equations are a great way to structure a numerical problem, but you gotta be mindful.

When using this type of structure, the more number-oriented candidates tend to just focus on the numbers and ignore reality. Don’t fall into this trap. You’re not being hired to simply find the right formula. Be mindful. Go a level further – why are we hiring more people? What drives hiring costs?

Let me show you how.

Here are two structures for the same problem: a company’s hiring costs are going up. What do you see? Which structure is better and why?

Notice how these structures are like an equation. “# of hires” * “Cost per hire” = “Hiring Costs”. “New hires to replace leaving employees” + “New hires to grow the company” = “# of hires”. Finally, the “Cost per hire” = “Cost to bring in a new candidate” + the “Cost to select new candidates”.

Equations are clear and accurate. Precisely what you’re looking for when doing MECE.

But do only the algebra and you sound like Dr. Obvious. To generate real insight, you should go a level deeper and mention a few qualitative issues that drive each numerical variable of your structure. No need to be MECE here, although you could if you combined Conceptual Frameworks with Algebraic Structures (I’ll show you how in Part 8).

Breaking down your problem as a formula may seem simple, but don’t ever underestimate its power nor how hard it is to come up with the right equation. Most candidates can’t. Yes, even the Harvards and PhDs of the world.

Doing it consistently will help you effectively solve real problems, and to communicate what you’ve found and what should be done. But to make it a habit and pull it off consistently in case interviews is harder than you think. Even the most analytically inclined candidates have a hard time seeing they can break down a metric as a formula in order to structure a problem.

(Here’s a few examples of structures that can easily be created by making equations – a lot of candidates would be stuck with these case questions, or would just wing it without structures.)

### But beware, there are two limits for these types of structures. You can’t use them in purely qualitative cases and they’re hardly the best option in long-term, strategic cases.

It would be a beautiful world a world where every problem could be solved with an equation. For an engineer at least, for god’s sake.

But that’s not the world we live in. Here on planet earth things don’t work this way. And in consulting world two types of problems aren’t well solved with these structures.

The first kind is purely qualitative problems. Because these structures rely on numerical variables, you can’t use them. Examples of these cases are: “what are the risks of such a move” or “what would a customer take into consideration when deciding to buy a certain product?”

For these qualitative problems, you can use either Process structures or Conceptual frameworks, the other two types of core structuring techniques we’re gonna see next.

The second type are long-term oriented strategic questions. M&As, Market entries, Long-term growth strategies, etc. Although you *could* use algebraic structures here, they’re typically not the best option. When thinking long-term, the numbers don’t mean much. In real engagements you can’t even *find* the numbers. Not even McKinsey has a crystal ball to predict the future. The most important things are qualitative and the relationships between the numbers.

For example, you can’t know what Coca Cola’s revenues and market share will be in the far future, but you can assume their brand will still be recognized, that their distribution footprint will be better than their competitor’s. You can also know some numerical relationships will be true: that the higher your price, the lower your market share; that the lower your costs, the cheaper you can charge.

The focus on these long-term problems should be on the qualitative issues and the relationships between the variables. Anyone trying to predict profits or other performance metrics without considering those is being delusional. To take that into account, anytime you get a case like that, consider using a conceptual framework instead.

### . . .

Algebraic structures are all about using the power of equations to be accurate and clear when structuring a problem. It’s a great, underused skill. But you can’t solve every problem in the world using math. We’ve seen a couple of cases where you’ll stumble upon problems if you try to do that.

To avoid getting stuck on those, you need to learn two more *core* structuring techniques: Process structures and Conceptual frameworks.

In Part 4, I’m going to show you how to use Process structures to fix all sorts of problems in a company. It’s incredibly simple and easy to learn. Actually, by the time you’ve read the article, you’ll *know* how to do it and have a remarkable new tool in your arsenal. The best part? Even though real consultants use it every day, because it’s not in any books, no candidate ever uses this.

JLJ

Hi Bruno

Thanks for a great article!

I have one clarifying question. Would the below be considered MECE? Isn’t it possible (and perhaps even likely) that the “customers we stopped serving” also “moved to the competition” and therefore would fall into both categories, e.g. not mutually exclusive?

Customer evasion = “Customers we ourselves stopped serving + customers who moved to competition + customers who stopped using this type of service”

Bruno Nogueira

Hey JLJ,

You’re right, but it’s a wording issue (my fault):

– “Customers we ourselves stopped serving” should’ve been stated as “Customers we’ve canceled our service to due to our own reasons”

– “Customers who moved to competition” should’ve been stated as “Customers who voluntarily decided to move to competition for their own reasons”

It’s the kind of thing that wouldn’t really matter in an interview because the interviewer would be a bit confused and asked what the candidate meant.