There Is No Advanced Math Required in Case Interviews, but Calculating Quickly Is a Real Challenge
Nearly all the math required in a case interview is arithmetic: addition, subtraction, multiplication, and division. You will likely need to perform these calculations with percentages, decimals or fractions, and calculate a percentage value (which requires division). Most candidates understand these math concepts; the challenge for many people is performing multiple calculations with large numbers quickly and without calculators or spreadsheets, in a high-pressure environment with a six-figure salary and your future career on the line.
If practiced, the maths part of the case interview can be completed competently and without much stress. Demonstrating good maths skills can be your differentiator in your interview so it is worth spending the time to practice. Being quick is not only a major plus for your performance but it also helps keep a natural flow to your interview, helping you build rapport with your interviewer.
Good mental maths skills are particularly useful in market sizing/guesstimate questions and consulting case studies.
Case numbers are “round” with few significant digits
The good news is that most of the numbers you encounter in case interviews (what we call “Case Numbers”) are “round” numbers and have only a few significant digits (i.e. only a few digits are non-zero), but may be in the Millions or Billions. For example, the number 200 Thousand, which is 200,000 in long-form, has a single-digit that is not zero (“2”), and so has one significant digit. The number 2.5 Million, which is 2,500,000 in long-form, has two non-zero digits (“2” and “5”) and therefore has two significant digits. Case numbers frequently have only one or two significant digits, less frequently three significant digits, and in rare cases four or more significant digits. The term "Case Calculation" refers to a calculation required in a case interview, and may provide specific Case Numbers or refer to a general calculation without specifying the numbers involved, such as calculating Revenue, given Price, and Quantity.
Here are some examples of the types of questions you would get in a case interview:
Q. A hairbrush manufacturer has fixed costs of £3,000,000 and they sell 175,000 units a year, what is the fixed cost per unit?
A. £3,000,000 ÷ 175,000 = £17.1
Q. A global software company sells products in Germany, France, and the US. The German market had revenues of £2.35bn last year, France had sales 23% higher than Germany, what were their total revenues?
A. £2.35bn x 1.23 = £2.89bn
Maths skills take practice but before you begin your practice it is best to choose calculation methods that you are most comfortable with. The method that you were taught when you were younger may not always be the method you want to use now.
Below we have found some methods that we think are good for speed and accuracy in pressure situations along with any useful tips or shortcuts that we are aware of.
Addition and Subtraction
Most of the Case Numbers you need to add and subtract will have only a few significant digits. If they have more than one significant digit, the last or “trailing” significant digits will often be “5” or “25,” which makes them easier to add/subtract.
Example 1: Add 250 Million, 300 Million, and 150 Million.
Answer: 700 Million
In this additional example, the leading digits (prior to the Million) are: 250, 300, and 150. These numbers have either one significant digit (300) or two significant digits, where the last significant digit is a “5,” which makes addition easier.
When you need to add Case Numbers with three significant digits, the last two significant digits are often “25” or “75,” which are also easy to calculate with.
Example 2: Add 225 Million, 375 Million, and 200 Million.
Answer: 800 Million
You may need to add some Case Numbers with three significant digits that don’t end in “25” or “75,” but they most likely end in “5.” For example, you might need to add numbers like 115 and 165. Since these numbers both end in “5”, they are relatively easy to add without a calculator, and the answer is 280.
It is highly unlikely you will need to add or subtract a series of numbers with three or more significant digits, where all the digits are effectively random, such as 147, 368, and 434 (where the last significant digits are not “25” or “75”).
However, if you have to do so, we recommend the regrouping method.
Candidates also need to understand compound percentage growth and how to make approximations with compound growth. It is a very common Case Calculation to be given a firm’s revenue (or another metric), and the associated Compound Annual Growth Rate (CAGR), and be asked to estimate that value at some point in the future.
Net Present Value (NPV)
Another common Case Calculation involves assigning a financial value to monetary payments that will occur in the future. Management Consultants usually determine the current value of future payments using a financial method called Net Present Value or NPV. Hence, candidates need to be able to calculate the NPV under a variety of scenarios.
NPV Example 1: How much would your company be willing to pay for another company that generates $20 Million in profit annually, if your firm requires an annual Return on Investment of 10%?
Answer: $200 Million
NPV Example 2: A real estate development firm is evaluating a project that involves buying a parcel of land and building condominiums on that parcel. The company forecasts they can sell the condominiums for a total of $250 Million six years in the future.
What is the maximum the real estate company would be willing to spend now to buy the land and develop the condominiums, if all the associated costs for the project would be incurred today, and they require a 12% annual return on invested capital?
Answer: $125 Million
More Useful Tips
Tackling questions like this can be daunting. To learn how to approach questions like this, have a look at our 5 top tips:
1. Don’t worry about getting the EXACT answer
It is important to remember that the interviewer is unlikely to be directly testing your maths skills, they just want to see how you approach the question so finding the answer to 5 decimal places is not important. They will usually be happy with an approximate answer, especially if it makes your calculations quicker.
2. Round the number
If you have the choice, make the numbers easy for yourself. As an example, it is helpful to take the UK population as 60 million rather than its true value of 66 million. They are not always looking for perfect answers, just a good thought process and rough figure.
3. Shorten long numbers
If you have the opportunity to write down the numbers, shorten a thousand to ‘k’, million to ‘m’ and billion to ‘b’. This will help you write faster and keep the numbers smaller as too many 0’s can be confusing.
4. Verbalize your reasoning to the interviewer
Explain out loud the calculation you are about to make. The interviewer may agree it is the right direction, they may give you part of the answer, or they could course correct and push you to a different part of the problem. It is important to give the interviewer the opportunity to help you as much as possible.
5. Make reasonable assumptions
Often you will be asked questions in which you are required to come up with the numbers yourself. These questions do not test accuracy but test your logic skills and common sense. As long as you are clear about the assumption you are making e.g. Every person living in the city gets their haircut once a month, then the interviewer can see your logic and challenge it if they think they need to.
Make sure to not only read through this article but to actually practice! There are a number of resources out there to help you with your maths skills and to improve your performance:
PrepLounge Mental Math Tool - interactive and user-friendly tool to train your case interview math with respect to all basic operations (e.g. addition, multiplication, percentage). You can even compare your performance to the overall PrepLounge community!
The Khan Academy - the website and app provides videos and practice for all your maths needs. They have exercises for all different levels and on an extensive range of topics.
BBC Skillswise - BBC has curated lessons to help adults gain skills for the workplace. Their maths skills section provides a good overview of the maths skills you would need.