Case Interview Math (Mental Math) Tools, Formulas and Tips
Consulting case interview mental math practice is a must as part of one’s overall consulting case interview preparation. All management consulting firms, and certainly McKinsey, BCG and Bain, expect candidates to be very comfortable with quantitative data, statistics, and the ability to make decisions and client recommendations based on data.
Management consultants at firms like McKinsey, BCG, Bain, Deloitte spend a lot of time working with numbers, charts, calculations, financial models in excel and other math work, often mental math work. So any consulting case interview mental math test, and there are really multiple mental math tests scattered throughout the consulting case interview process is something you have to be well prepared for.
This does not mean that you need to have a math degree to have the right level of consulting case interview mental math skills. But you do need to know what is expected of you and you do need to practice mental math a lot.
How is consulting case interview mental math different from academic math?
Because management consulting is all about solving difficult problems, usually under extreme pressure, the case interviewer is expecting a candidate to approach math problems in a specific way. In academic settings the most important element of solving math problems is accuracy. Accuracy is also very important for case interview math but management consultants usually work under extreme time pressure. And so answers are often required to be close enough to guide towards the “right” recommendation, versus being 100% accurate.
For example, imagine you are asked to calculate the market size for baby diapers for sensitive skin in Singapore. If this was a problem within an academic setting you would be expected to give an accurate answer correct to the decimal point. In consulting case interview settings you will have to make many educated estimations to arrive at, hopefully, a close enough answer. And then you will be expected to do what we call a sanity check to ensure that your answer actually makes sense.
Let’s take a look at an example from a real McKinsey engagement, mentioned by one of our trainers, Kevin P. Coyne. In case you don’t know, Kevin is a former McKinsey worldwide strategy practice co-leader and he leads The Consulting Offer II, which you can access if you join our Premium membership or FIRMSconsulting Insider level.
In this example, Kevin mentioned serving a large bank and during initial interviews with employees of the bank, Kevin’s team noticed that 100% of the profit for that bank was coming from one business unit. That does not mean that all other business units were operating at a loss. But combined all other business units of that bank had zero profit. So the bank was dependent on this one unit to generate all their profits.
Kevin’s team further uncovered that a lot of clients that the unit served were really old. To give a more accurate answer on how bad the situation was Kevin’s team selected only 1 letter in the alphabet and studied the age of all the clients whose name started from that letter, let’s say it was letter B.
This exercise uncovered that within the next 5 years that bank would lose something like half of its clients. And it does not mean the bank will have those clients for 5 years and then they will disappear. No, the clients will start dying now and within 5 years the client base will be about half smaller than now.
And younger people were not interested in that type of service. Doing the same analyses for all clients within the unit would be cost-prohibitive and will take significantly longer, and the limited analysis conducted was more than enough to understand that the bank was in serious trouble and drastic action was required.
This is a great example of how math in real consulting settings is often focused on getting close enough/good enough answers fast and cheap. And as a great management consultant, you will need to have strong enough business judgment to know what is good enough and what is required and to never waste the client’s money and other resources on unnecessary analyses.
Strengthening your mental math and written math skills is one of the most important elements of preparing for case interviews.
As part of a case interview process, your mental and written math skills will be tested in multiple ways. If you are strong in academic math you are in a good place. However, the style of math used during case interviews is quite different vs. math problems in the academic context, as we discussed above, and takes time to get comfortable with.
Some examples of what case interview math test can include:
Case interview math test can include word problems. Word problems used as part of case interviews are similar to the type of word-based problems you practiced for as part of your GMAT preparation or preparation for other standardized tests. And such a case interview math test may or may not include a business-based context.
Case interview math can be tested during a full case. In fact, full cases almost always test math along with other skills. For example, coming back to the example above, you may be asked to estimate the market size for diapers for sensitive skin babies in Singapore as part of a full case of your client considering entering the Singapore market. As part of the case, you may also be asked to work with many graphs and charts, which we refer to as data cases. We cover data cases extensively in The Consulting Offer, our flagship program where we help real candidates prepare for interviews with McKinsey, BCG, Bain, Deloitte, etc. You can track candidates’ preparation at various stages, all the way from networking, editing resume and preparing for standardized tests to getting an offer and deciding if they should accept an offer. You can track Ritika joining McKinsey Chicago, Jen joining Bain Boston, Assel joining McKinsey Europe after 5 years out of the workforce and with no prior work at MBB (never before been done), Sanjeev joining BCG, Alice joining McKinsey NYC and much more.
Mental math is also tested as part of case interview math tests. In fact, it is tested a lot as part of the case interview process. You will be required to do math in your head and very fast. This is often one of the most difficult components of a case interview for candidates. The Consulting Offer will help you prepare.
Standard math such as multiplication, division, fractions, percentages, and other concepts are routinely tested. Case interview math tests are usually baked into a case and math is just a component to finding a solution within a specific business context.
In all examples of case interview math above, speed and relative accuracy matter. And the use of calculators is not allowed. So it is crucial to practice and be ready to handle case interview math tests fast, accurately, and without a calculator.
Consulting case interview math formulas
Revenue = Volume x Price
Cost = Fixed cost + Variable cost
Profit = Revenue – Cost
Profit margin / Profitability = Profit / Revenue
Return on Investment (ROI) = Annual profit / Initial investment
Breakeven / Payback Period = Initial investment / Annual profit
EBITDA = Earnings Before Interest Tax Depreciation and Amortization. EBIDTA is essentially profits with interest, taxes, depreciation and amortization added back to it. It’s useful when comparing companies across various industries.
What will help you become faster in doing mental math during consulting case interviews is rounding numbers. For example, ~82 million population of Germany becomes 80 million, ~46.7 million population becomes 45 million. The key to rounding numbers is to round them carefully, in a way that does not distort too much the final answer. A good guideline to follow is not to round by more than 10%. It is also helpful to round both up and down as you are working through the case, so the effects, to some degree, cancel each other out. At the end also make sure you check if your answer actually makes sense.
Fast mental math: dealing with large numbers
The key to dealing with large numbers, like 200 million, for example, is to remove zeros and then add them back later. Use labels (m,k,b) to help you keep track. So if you have 200 million, it becomes 200 m to help you remember that it is millions. 200,000 will be 200k. 10 billion will become 10 b. The key to achieving fast mental case interview math is to simplify. For example, 5 x 30 million becomes 5 x 3 = 15 with 7 zeros.
Fast mental math: break down numbers into smaller parts
When dealing with case interview math, another trick that will help you work through the problem faster is breaking down numbers into smaller parts. For example, 14 x 6 = (10 x 6) + (4 x 6) = 84.
Fast mental math: subtracting from numbers with 1 followed by zeros
This is another trick for faster case interview math. Again, simplify. 1000-536 becomes 999-536+1 = 464.
Fast mental math: group numbers into multiple of 10 (addition)
Another trick for fast case interview math is to group numbers into multiple of 10 (for addition). 3+7 + 4 + 6 +13 +7 +21 becomes 10 + 10 + 20 + 21 = 61.
Other tips to achieve fast case interview math (mostly mental math) during a consulting case interview
Here are a few tips to keep in mind to help you perform better during a consulting case interview when it comes to case interview math (and mostly mental math).
At the beginning of the case ask your interviewer if it is ok to round numbers. Most of the time they will say yes and it will make math calculations much easier and faster.
Do not rush. If you make a mistake it will take you even longer to fix it. This is if you even catch your mistake. You may also catch your mistake by the time when the interviewer will not give you an opportunity to fix it. And case interview math mistakes can be very embarrassing and lead to a completely wrong recommendation. Of course, there is a lot of time pressure during consulting case interviews so do not take any longer than you need. You need to find a good balance. This comes with a lot of practice. We provide a lot of opportunities for you to practice case interview math. Some full cases are provided below and you will find more on our YouTube channel. And, of course, you can unlock access to all candidates and seasons of The Consulting Offer when you become Premium member (more details below).
Do not be afraid to write things down when you feel you need it.
Keep your writing organized. Let say you are estimating how many cars will be purchased in Germany in 2020. As you are putting down numbers for each element of your equation keep it neat and organized so you don’t get confused and it will also help you avoid silly mistakes.
Do not state your answer to an interviewer as a question. Be confident in your answer.
As part of your preparation refresh key math topics like ratios, fractions, percentages, averages, and probability. Khan Academy is a great place to refresh your math skills. And you will have more than enough opportunities to practice fast mental case interview math as you go through various candidates and seasons within The Consulting Offer (part of Premium membership).
Practice consulting case interview math / mental math with full cases
As you work through the cases remember to focus on all elements of good case performance, not just math. People usually underestimate how important other elements of case interview preparation are, including FIT. And only realize after being rejected that the elements they ignored during preparation were the reason for the rejection. Learn from the mistakes of others. Take all elements of case interview preparation seriously.
BUSINESS CASE EXAMPLE #1: MCKINSEY, BAIN, BCG ACQUISITION CASE
This case is a McKinsey style case, of medium level difficulty. It should take you 15-20 minutes to solve this case.
The question is given upfront, at 2:02. The part in black is the part the interviewer would share with you and a part in grey is the part interviewer may share as the case progresses. The interviewer wants to see if the interviewee understands the case and asks the right questions.
The case question is quite explicit but even so we will show you how you can adjust the case and make the case more explicit.
Everything rests on the key question. If anything is not part of the key question, ignore it. Even though lots of information is provided, take time to understand and set up the case.
Always show why information is needed, and show progress so the interviewer is they are willing to provide more information. It is a barter. And always use the case information provided and the appropriate language to push the case forward.
BUSINESS CASE EXAMPLE #2: COMPREHENSIVE MARKET ENTRY CASE
We did this recording a few months after we completed the training with Rafik (TCO I). This is one of the most complex market entry cases we had to put together. It has elements of operations, elements of pricing, elements of costing and, obviously, elements of market entry. And it is probably the most difficult market entry case we can do because most market entry cases that most interviewers focus on have a strong market attractiveness element, market profitability element. But very few people actually look at the operational issues of entering the market. And it does not matter who you are interviewing with: Bain, BCG or McKinsey. The bulk of the focus usually goes towards analyzing the market worthiness but not a lot on the operational issues. So we decided, in this case, to flip it around and give this case a strong operational theme.
BUSINESS CASE EXAMPLE #3: PEPSI’S LOS ANGELES BOTTLING PLANT
Operations cases can be tackled in two ways: strategy and operations and within operations from productivity and the supply chain side. This case uses the supply chain side.
This case is candidate-led. As we mentioned above, candidate-led cases are much harder than interviewer-led cases. That is why we at FIRMSconsutling place so much more emphasis on teaching you how to lead cases vs. relying on the interviewer to lead. This will be considered an operations case. Pay attention to a very insightful brainstorming at 14:50 which includes at least one idea you most likely would not come up with if you were solving this case before watching this video.
What else can I do to improve my case interview math?
Mental math is a muscle. But most of us do not exercise it enough once we leave school. So your case interview preparation needs to include math training.
First refresh your knowledge and ability to calculate basic multiplications, divisions, additions, and subtractions, without a calculator. The Consulting Offer program (a part of Premium membership) includes ongoing opportunities to practice this. We also have many cases available for free on the FIRMSconsulting YouTube channel to get you started.
And there are other tools you can use for case interview math prep.
Khan Academy has some resources that you may find helpful. Here are some helpful links:
You will need to regularly practice to get comfortable with mental and written math. Case interview math tests require you to do all math calculations fast and accurately. We recommend working through a few sessions of The Consulting Offer a day to ensure multiple opportunities to practice math and other skills you need to give yourself the highest chance to get an offer from firms like McKinsey, BCG, Bain, Deloitte, etc.
Go through a few sessions every day and you will start feeling more comfortable over time not just with case interview math but with your resume, networking, estimations, brainstorming, answering FIT questions in a way that answers what the interviewer is REALLY asking you.
You will also develop or strengthen the ability to lead and handle difficult cases, and the ability to develop your own framework uniquely tailored to solve a particular case, and much more. View it as an investment in skills that will serve you for the rest of your life vs. just searching for tips and tricks to get an offer from McKinsey, BCG, Deloitte, et al.
Additionally, some candidates found the following tools helpful as supplemental materials along with The Consulting Offer. We have not tested those tools but are sharing them in case you would like to explore them.
Mental math games (Android). This one is similar to the mental math cards challenge app on iOS (below).
You will need to get comfortable doing calculations fast and accurately. And this comes with a lot of practice. If you will be using The Consulting Offer to prepare for your consulting case interviews you will have what seems to be never-ending opportunities to practice mental and written math as part of the full cases and as part of particular questions such as estimations, etc.
Management consulting jobs are very competitive, and working with FIRMSconsulting can mean the difference between getting an offer, or multiple offers, from your target firms and barely getting an offer from the company you hoped you never would need to settle for. And the latter example is something I, unfortunately, observed many of my MBA classmates settled for.
When it comes to case interview math The Consulting Offer program, all 5 seasons of it and counting, with various candidates, includes everything you need to master not just case interview math, but all key aspects of consulting case interviews.
Don’t miss out by investing your time with general math drills when you can practice real-world case interview math examples while being taught by former consulting partners.
If you want the most comprehensive guidance for consulting case interviews math, and other aspects of case interview preparation, so you go to your interviews confidently, become a Premium or FC Insider level member now. And if you still have questions contact FIRMSconsulting ([email protected]) to find out why candidates even from top schools like Harvard, Stanford, and MIT choose us when they need consulting case interview preparation help, and stay with us for years and years once they get coveted jobs at McKinsey, BCG, Bain, Deloitte, etc.
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Case interview resume template used in The Consulting Offer. Offers from McKinsey, BCG, Bain et al.