**Case Interview Math – Know THIS Before Your Consulting Interview**

- Last Updated February, 2020

## Table of Contents

Are you nervous about solving math problems in the middle of your consulting interview?

Don’t worry. You’re not alone.

Luckily, typical case interview math problems aren’t hard. They’re basic algebra – addition, subtraction, multiplication, division, and fractions/percentages. They can also involve extracting data from tables and interpreting it. All the math you need you covered by age 13–and if you need to brush up, we’ve got you covered.

You’ll find consulting math easier if you know what type of problems to expect and follow our** 4-step approach to minimizing case interview math mistakes**.

If this is your first visit to MyConsultingOffer.org – head to Case Interview Prep for an intro to the management consulting interview process.

If you’re familiar with what a consulting case interview is, and want a preview of the math you’ll need to succeed in consulting interviews, you’re in the right place.

Let’s get started!

**Why Do Consulting Case Interviewers Care about Math Skills When Everyone Has a Calculator in their Phone?**

Imagine you’re sitting around a conference table with your case team and client discussing how to solve the client’s business problem. You might be trying to figure out where to look for cost cuts that could improve the client’s profitability:

*Example: A manufacturing company wants to improve it’s profit margins to 20%. Should we start by focusing on operations or research and development to find costs that can be cut to achieve this goal?*

Or you might be discussing which new market will give the company the revenue growth they want to achieve.

*Example: Should a North-American-based laundry detergent company launch their product into the European or Latin American market to find an incremental $20 million in revenue?*

There are qualitative issues to consider when addressing either of these questions, such as what are the business risks related to cutting costs in operations vs. R&D? Or what does competition look like in Europe vs. Latin America?

But answering these qualitative questions will require research and discussion. Simple, back-of-the-envelope calculations can often ensure this research and discussion are worthwhile.

This is important because a week of a consulting team’s time costs a lot of money. Doing a quick calculation to make sure the team is pursuing a strategy that will solve the client’s problem is important.

*Example: Can we save enough money in either operations or R&D to meet our profit margin targets?*

If a quick calculation shows that R&D expenses are only 20% of operations expenses and that you would need to cut the department entirely to reach the margin improvement goal, that tells the team that the team should first focus on cost improvement in the larger operations budget.

*Example: Is the laundry detergent market in Europe large enough that we could meet our revenue goal of $20 million by entering it? How about Latin America?*

If the Latin American market for laundry detergent is not large enough to support a new competitor capturing $20 million in revenue, then focus should first be given to the European market. This type of assessment can quickly ensure the team focuses its efforts on a solution that’s likely to have a positive outcome.

**Consulting Math: 4 Types of Problems**

Examples:**Market sizing**

What is the size of the market for laundry detergent in Latin America?

How many pizza pies are consumed each day in Pittsburgh?Examples:**Financial calculations**

What are XYZ company’s profits?

What is XYZ company’s profit margin?

What is XYZ company’s market share?

What is XYZ company’s growth rate?**Investment analysis**

Example:

How many years would it take to break-even on an investment?

What is the return on investment?**Operations problems**Example:

What is the capacity (of a factory, machine or worker)?

What is the utilization rate?

Watch this video to learn how to master case interview math. For reference, I’ll also provide key formulas and examples below.

**Case Interview Math Examples**

**Financial Calculations**

Here are the key formulas you need to know:

- Profits = Revenue – Costs
- Profit margin = Profits/Revenue
- Market share = Revenue for XYZ company/Revenue for all companies in the market
- Growth rate = (New – Old) /Old

So Revenue growth rate = ( this year’s revenue – last year’s revenue) / last year’s revenue

Here are some examples of financial math calculations:

- A firm with $100 million in revenue and $80 million in costs has profits of $20 million.
- A firm with $20 million in profits and $100 million in revenue has a 20% profit margin.
- A firm with $100 million in revenue in an industry with $400 million revenues has a 25% market share.
- A firm that made $100 million this year and $90 million last year had an 11% growth rate.

**Investment Analysis**

Here are the key formulas you need to know:

- Break-even: Investment cost / annual profit = years to break even
- Return on investment (ROI) = (Revenue – investment costs) / Investment cost

Here are some examples of investment calculations:

- A company spends $10 million in costs to enter a business with annual profits of $1 million has a 10-year payback.
- A company that will earn $12 million on a business that it paid $10 million to enter had a 20% ROI.

**Operations Problems**

Here are the key formulas you need to know:

- Capacity in units = total capacity / capacity required to make one unit
- Utilization rate = actual output / maximum possible output

Here are some examples of operations math calculations:

- If a machine that can produce a widget every 5 minutes, it has a capacity of producing 96 widgets in an 8-hour shift. 8 hours * (60 minutes/hour) / 5 minutes = 96.
- If the widget machine is left unmanned while the operator is at lunch (1 hour) and during breaks (2, 15 minutes each), then the machine will only make 78 widgets. 78 widgets / its capacity of 96 means it ran at a utilization rate of 81.25%.

**Market Sizing Math**

When Davis, founder of My Consulting Offer, was preparing for his interviews, he frequently practiced his market sizing skills at dinner. One night, his friend challenged him to estimate the number of potential bachelors available for her. In this article on Market Sizing Questions, Davis walks step-by-step through his assumptions. Here, he walks through the actual calculations:

My friend attended college with me. She was a non-American student and I knew she wanted to marry someone who could give her American citizenship, so I started with the **US population – 320 million**.

Then I cut the population in half to focus on men since she was interested only in men. **320 million / 2 = 160 million.**

To rule out men who were too old or too young for her, I cut the population of men into age groups. **The average life expectancy in the U.S. is 80 years. I wanted to focus on only men 20-30, so 1/8 of the U.S. male population. 160 million / 8 = 20 million.**

I also wanted to focus on men that were taller than her, but actually, my friend is pretty short. Almost all men in the right age range are taller than her so there was no need to factor that into my calculation. **Men 20-30 who are taller than Davis’s very short friend = 100% or 20 million.**

Next, I looked at attractiveness: both the portion of the target male population that my friend would find attractive and the percentage of those guys who would find her attractive.

This friend’s pretty picky. She was only interested in guys who were 9’s or 10’s on a scale of 1 to 10, so about 20% of the population. **20 million men aged 20-30 * 20% who are really hot = 4 million.**

I decided to be conservative and assume only 10% of the population my friend thought was attractive would also find her attractive. **10 % of the 4 million hot guys age 20-30 would find her attractive = 400,000.**

My friend wanted a guy that had a good income, so I decided to focus on people attending or who’d graduated from college. In fact, she was *really* picky, so I decided to focus on top colleges like the Ivy League schools. **About 1% of the U.S. male population attends highly competitive schools like the Ivy League. 400,000 * 1% = 4,000.**

Finally, I assumed many of the guys who were in the right age range *and* who my friend found attractive *and* who found her attractive *and* who went to a top college might already be taken. I cut the number I’d come up with in half to reflect the highly eligible guys who were already off the market.** 4,000 hot, really smart guys age 20-30 / 2 = 2,000.**

My **“so what”** based on this analysis was that my friend might want to be a little less picky. All her requirements brought the number of eligible bachelors down from 160 million to only 2,000. But she thought that a group of 2,000 guys was plenty for her to find Mr. Right in, so she decided to keep her standards high.

**4 Steps to Minimizing Mistakes in Consulting Math**

It’s hard to do math under the pressure of an interview. These steps are the key to keeping your math accurate.

**Be clear on what the calculation will tell you. Don’t just start doing calculations. Know what business problem you’re trying to solve and how your math will give you insight so you can make a decision. Share this with your interviewer.****Structure your approach.**Before you do any calculation, walk through the steps you’ll take to answer the question with your interviewer. There are frequently several steps in consulting math problems.**Do the calculation step-by-step.**Once you have your approach to the case math problem, do one calculation at a time to ensure accuracy.**Explain the “So what?”**Don’t wrap up your answer with just a number, explain what the number means in the context of the business problem you were trying to solve. What would you recommend to the client?

Here’s an example:

*A manufacturer of high-quality wood outdoor furniture is considering extending its product line to include Adirondack chairs. It only wants to enter the market if it can make at least $5 million a year.*

Data provided:

*The size of the North America market for Adirondack chairs is estimated to be $1 billion. The top 4 players hold 20% market share between them. Profit margins average 20%. *

Now apply the 4-step approach for minimizing mistakes.

**Be clear on what the calculation will tell you.**“I’d like to calculate likely market share and profit our client could expect if it entered the market for Adirondack chairs in order to see if the opportunity is large enough to meet their criteria of $5 million profits.”**Structure your approach. “**To do this calculation, I’d first look at the likely market share our client could achieve based on the share of the top 4 players in the market. Then I’d calculate the revenues that they could expect by multiplying the market share by the size of the market. I’d then use the industry’s average profit margin to calculate the level of profit they could expect.”**Do the calculation step-by-step. “**The top 4 players in the market for Adirondack chairs have a combined market share of 20%. 20% market share /4 players = an average market share of 5%. Based on the client’s success in the wood outdoor furniture market, we expect they could achieve this level of market share as well.”

A 5% market share in a market with $1 billion in annual revenue would give the client $1 billion * .05 or $50 million in revenue.

$50 million in revenue for a product with a 20% profit margin would give the client $10 million in expected revenue.”**Explain the “So what?” “**Based on these calculations, the client should consider entering the market for Adirondack chairs because the expected annual revenue of $10 million exceeds their minimum criteria of $5 million.”

**More Case Interview Math: Extracting Data from Charts**

In some cases, particularly when a case interview math problem is one step in a multi-step case question, an interviewer might hand you a chart with key information on it. These charts often have more pieces of data on them than you need. You need to find the right data. Or, you may need to manipulate the data to find what you need.

For example, a table might provide a company’s costs and revenues when the information you need is profit margin. Or, it might provide the revenues of the top 4 companies in the market and a 5th number that totals the revenue of all other players in the market, but you might need market share for player #3.

Don’t let all the number on the chart throw you. You’ll still be using the same basic formulas to analyze these numbers.

Instead, take a minute to understand the information the chart provides and explain it to your interviewer. Then proceed with the case interview math problem as described above: be clear about what you’re looking for in the calculation, walk the interviewer through your approach, do the actual calculation, and then provide the “so what.” Using this approach will make interpreting data tables in an interview straightforward.

**Critical Numbers to Know for Case Math Problems**

**Links to Bain, BCG and McKinsey Resources on Consulting Math**

Want to hear more about the importance of case interview math straight from the top management consulting firms? Bain and BCG list quantitative analysis as part of what they test for. McKinsey provides examples of the type case math in its case interviews in this practice test.

On this page, we’ve covered the typical types of case interview math problems you’ll see, explained how to extract data from charts, and provided tips on minimizing your consulting math mistakes. These skills will help boost your confidence in management consulting interviews and ensure you ace your case.

People who are working on their consulting math skills typically find the following other My Consulting Offer pages helpful:

- Market Sizing Questions discusses a type of case study interview question that always tests math skills.
- Types of Consulting Case Interviews provides an overview of all the types of cases you can expect to see.
- Case Interview Examples provides example cases you can use to practice.
- Case Interview Practice provides tips to make your practice time as efficient as possible.

We hope this page has increased your confidence in tackling consulting math problems! **Comment below on the types of consulting math problems you find the toughest.** We’ll provide tips from our coaches.

**Help with Case Study Interview Preparation**

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