Case interview maths
Case interview maths is not the same you find in online tests. The maths skills that you will require you start learning at a young age such as addition, subtraction, multiplication, division, and percentages.
The main difficulty with case interview maths is you will be working under pressure with big numbers such as multiplying 70,000 by the 356 days of the year without a calculator.
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.
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 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.
The regrouping method aligns the two numbers on top of each other by their units and then you sum each unit column to find the total number. It reduces the complexity of the equation down to single digit additions and can be used for decimal places too.
The long subtraction method we prefer is built on the same principle as the long addition and so you don't need to learn a new method but rather apply it differently. The two numbers are again aligned on top of each other and instead of summing each column you subtract the two numbers.
For subtraction it is important that the larger of the two numbers is on top.
Long multiplication methods have the most variance of the calculations but most follow the simple principle of breaking the large numbers into its component parts e.g. 728 is 700, 20 and 8. To keep things as similar as possible across the different calculations we again choose to work vertically with the numbers aligned by units.
Division gets most difficult when dealing with decimals but the method we prefer allows you to continue into decimals seamlessly, this is particularly helpful when dealing with small amounts of money e.g. $3850.45, the 45 cents make the calculation more difficult.
This method moves away from the vertically aligned method but we find it easiest and most versatile for long division.
Relativity is an important concept in consulting case interviews as a number on it's own does not demonstrate the numbers value in comparison to the other number(s) in the question. Being able to convert to percentages is an important skill and will often be required in case interviews.
There are a number of simple ways to find percentages but if you are stuck try finding 10%, 5% and 1% first, using a combination of these amounts you will be able to find other percentages fairly quickly e.g. 37% = (10% x 3)+5%+(1% x 2).
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 to test your logic skills and common sense. As long as you are clear 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.
See our market sizing page for more information about this.
There are a number of resources out there to help you with your maths skills.
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.
Magoosh Mental Maths (app) - the app has mental maths practice you can use on the go. The flashcard systems come in groups of 20 and work well for daily practice.
If you are confident with your technique and now looking to practice, we have put together 50 arithmetic questions in a free download that will test your case interview maths skills.
If you are ready to test your maths ability on consulting case interview style questions then our consulting multipack includes arithmetic, market sizing and case interview questions based on real life consulting interview questions.