# Consulting Interviews: How to Prepare for Mental Math Questions

Published: May 08, 2017

Great news! You just heard back from McKinsey and have been invited to round one internship interviews. For many candidates, this fleeting moment elicits an incredible hit of dopamine that fades just as quickly as it came on. Then a creeping realization takes over: it's been years since you've done any mental math—how are you going to handle all that case math?

Don't worry. If you find yourself in a similar quandary, this three-part "How to prepare for your case math" series is here to help you through it. In parts I and II of this series, we'll methodically walk through the top types of math questions to expect, provide context on why, and simple tips to help you ace them. Finally, in Part III, we'll share three simple tips to handle a math error and recover successfully.

Ok, now for some good news: case interview math isn't conceptually or theoretically difficult. There is no need for you to go on a mad scramble searching for your old calculus textbook or dust off your old quadratic equations formula. Case interview math is very conceptually straightforward. The difficulty stems from the computational aspect. Specifically, there are three key drivers that make it computationally difficult:

- The numbers themselves tend to be large, (ex: $125,000,000)
- The problems tend to require recalling and calculating with lots of different numbers
- The interview scenario itself adds pressure which tends to create nervousness which prohibits people from calculating accurately

Don't sweat it though; all three problems above can be mitigated by understanding what to expect, practicing and preparing the smart way and planning ahead on how to recover from an error, should you need to.

**What to Expect**

First, let's take a look at the usual suspects: what type of math problems should you expect and why?

- Large number problems, e.g. big multiplication or big long division
- Break even analyses
- Growth rates
- Market sizing

Let's get started with handling large numbers and breakeven analyses.

**Large numbers**

Many consulting cases will include really, really large numbers. It's not uncommon to find yourself dealing with numbers like 125,000,000 units, or $25,000,000,000 in revenue. You'll find yourself doing multiplications, percentages, additions and subtractions on top of them. Why? Well, the elite global consulting firms work with Fortune 1000 companies, who by their very nature of being included in that group, operate at significant scale.

*Sample:* If we believe the client can capture 15% of a $25,000,000,000 within five years of entering the market, what do we expect their revenue from that market to be?

When trying to keep all those zeroes straight, a very simple, useful tool can be placeholders. For example, the above question would become what's 15% of $25B. You've now substituted a "B" for all those zeroes - much easier to keep track of! Now you just need to calculate 15% of $25 which is $3.75. Thus, $3.75B is the answer.

You can use the same technique with long division: say you're asked to calculate the average price per unit a client realized, and you know that total revenue was $4 billion and 80 million units were sold. Again, you can use placeholders to re-write this problem as $4,000M revenue / 80M units. Now, your "M" placeholders cancel and you're left with 4,000 / 80, which is $50 per unit.

**Break-even analysis**

This is a perennial favorite of consultants. Why? Well, a key component of any consulting engagement is proposing a series of recommendations to solve the client challenge. In most cases, those recommendations will require financial outlays to set things in motion. Consider a hypothetical case where a firm recommends staffing and training a new sales team to sell an existing product into a new market. The client will certainly ask: "how long will it take to recoup the initial cost of setting up that sales team?" This is the key type of question a break-even analysis is designed to resolve!

*Sample*: If the client needs to invest $3,000,000,000 to enter the market, and expects to sell units at $1,500 and all in costs to produce each unit are $1,300, how many units does the client need to sell to break even?

For break-evens, the key thing is to setup the algebraic equation, and to do this you want to ask yourself two questions.

- First, what is the total investment that is required?
- Second, how much does each unit contribute toward that investment?

These two questions help set up your equation: investment = unit margin * units.

In this case, that gives us $3,000,000,000 = $200 * 15,000,000. Meaning that the client needs to sell 15 million units to break even.

It's important to notice that the equation uses the more general "unit margin" as opposed to something like (price - variable cost).

Why?

There are many flavors of break-even problem and while (price - variable cost) might be appropriate for the aforementioned example, it doesn't fit for all.

Consider the question: a partner plans to buy an Italian countryside bed and breakfast for $375,000 and estimates that hotel B&B revenues will be $100,000 with a 40% margin. Will she make her money back in 10 years? You don't have any price info! And that's OK if you think about it from the more general unit margin perspective formula above. Here the annual unit margin is $40,000 and the unit itself is years, not widgets, pianos, motorcycles, or whatever.

**Conclusion and next steps**

As with all things, using these techniques and frameworks becomes second nature with practice. Even if it seems unnatural or clunky at first, repetition and practice can be the key toward blazing through these types of math problems like they're cake. Stay tuned for Part II of this series where we'll walk through the same overview on growth rates and market sizing problems.

*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. *