How detailed should math calculations be?

case math Math problem
New answer on Jul 17, 2020
9 Answers
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Anonymous A asked on May 31, 2019

How detailed should we do math calculations?

Is it ok to use a pen and write down multiplication or division (as we used to learn in school) and do detailed but correct one or should we calculate in our head and write estimated number?

example:

2.7 x 3,600 =

7.5% of 85=

I am more comfortable to write down, spend 10 sec but to get a detailed answer, but not sure whether it is ok on case interview and interviewers need people who can calculate in their heads...

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Sidi
Expert
replied on May 31, 2019
McKinsey Senior EM & BCG Consultant | Interviewer at McK & BCG for 7 years | Coached 300+ candidates secure MBB offers

Hi!

I have written this earlier, and I will repeat it: the obsession with "Mental Math" is one of the many damaging nonsense myths that are flying around! Mental math is simply not something that is required in ANY way!

  • You are not tested for doing math stunts in your head, but for the rigor and correctness of your analysis.
  • You will NOT get bonus points for being lightning fast!
  • You WILL get bonus points for being very clear and easy to follow.

This means, the skill you have to build is to quickly identify what you need to analyze and why, and organizing this in a way that you can work through this in a very linear and easy to follow manner. Hence, I recommend to ALWAYS use pen and paper for your analysis (e.g., using tables works very well in many situations).

At the extreme, being exceptionally fast in mental math will even HURT your case performance! The reason is simple: the interviewer will always assume that the way you behave in an interview is also how you behave vis-a-vis a client. If you become a human calculator, doing all sorts of complicated math stunts lightning-fast in your head, then you become VERY HARD TO FOLLOW. Hence, the quality of your communication deteriorates. And this is always your fault, not the client's!

So in essence, make sure that you are doing clear and very easy-to-follow calculations, using pen and paper to write down the required steps first and then to perform the actual computation. Trying to becme a lightning fast human calculator has a lot of risks and practically no benefit.

Cheers, Sidi

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Francesco
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Content Creator
replied on Jun 03, 2019
#1 Expert for Coaching Sessions (3.600+) | 1.300+ Reviews with 100% Recommendation Rate | Ex BCG | 8+ Years of Coaching

Hi Anonymous,

it is totally fine to write down your answer and it is better to spend few more seconds to do so and provide the right answer, rather than be faster and risk not to be accurate with mental math.

To improve your math, you can consider the following tips:

  • Divide complex math in smaller logical steps: if you have to compute 96*39, you can divide it in 96*40 - 96*1 = 100*40 - 4*40 - 96*1 = 4000 – 160 – 100 + 4 = 3744
  • Learn shortcuts for fractions and exponentials: the most useful to know are:
    • Fractions: at least 1/6, 1/7, 1/8, 1/9
    • Cubes: ideally until 19^2
  • Practice: there are several online services you can find to improve your speed; I would recommend to keep track of the performance in an excel sheet to assess whether you are improving and if not, analyse the reasons for that

You may be able to round numbers in market sizing, although in cases the interviewer is usually looking for specific numbers; if that’s the case you won’t be allowed to round. I would recommend to always check with the interviewer upfront if you can do so to avoid misunderstandings.

Best,

Francesco

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Serhat
Expert
replied on May 31, 2019
BCG | Kellogg MBA |82% Success rate| 450+ case interview| 5+ year consulting | 30+ projects in ~10 countries

Hi there,

2 things are important for math calculations:

1- Accurate enough: You can do roundings where necessary if your answer is within the around 5% deviation range. Remember, cases you are doing could have been done in 3 months in real life but you are targeting to finish them in 30 minutes. So you should not spend a lot of time to make your calculations 100% accurate. Having said that it is important to communicate your roundings with the interviewer.

2- Pragmatic (fast): On the other hand, most of the times there are fast ways to do calculations and you can be both very fast and very accurate. If you try to do it 100% accurate by writing all as you were doing at school, probably it will take a lot of time. Let's continue with the example you proposed. You can do all in your head without writing anything. However you are free to write if you want to.

For 2.7*3600 what you can do is multiplying 3 with 3600 and then subtracting 10% of your result as 2.7 is 10% lower than 3. So, 3 times 3600 is 9000+1800=10800 (3 times 3k and 3 times 600). 10% of 10800 is 1080. So 10800-1080 is roughly 10000 or you can be more accurate and say 9720.

for 7.5% of 85, you can say that 5% is equal to dividing the number by 20. so 5% of 85 is roughly 4.2. If you add half of this number corresponding to 2.5% of 85, you will find 7.5% of 85. So 4.2+2.1=6.3 This level of accuracy is enough for the case interview.

Hope it helps.
Cheers
Serhat

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Ian
Expert
Content Creator
replied on Jun 01, 2019
BCG | 100% personal interview success rate (8/8) and 95% candidate success rate | Personalized interview prep

Hi,

In general, ask to round if the numbers seem unmanageable. Say something like "I'm going to round this number to 100 if that's ok". If they say no, then of course you're ok to write down the math! However, use a "scrap" math piece of paper so as to keep your "presentation" slides clean.

Fast math is not the focus of cases! We only practice fast math so that it doesn't distract us and become the focus!

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Daniel replied on May 31, 2019
Imperial College PhD, Rolls-Royce Project Engineer, RWTH Aachen Mechanical Engineer and Business Administrator, Software Engineer

Hi,

before you round off or estimate, ask the interviewer if s(he) is fine with it. You can always ask for time to do the math, but tell the interviewer what you are going to do in advance. Speaking out loud what you are doing helps the interviewer following you.

Best,

Daniel

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Vlad
Expert
Content Creator
replied on May 31, 2019
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School

Hi,

Just ask the interviewer: "Is it fine if I round it up that way?" and then continue if he is fine with that level of preciseness

Best

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Anonymous replied on Jul 17, 2020

Dear A,

It's ok to write down your calculations

Dear Chris,

Of course you can make it on paper. You have to do it to make you calculations clear and communicapable.

Consulting math is a very different than academic math. Working consultants - and consulting interview candidates - are always under time pressure. Results are what matter and answers are required simply to be good enough to guide business decisions, rather than being absolutely correct.

Also remember here about estimating and adjusting.

For example: 96,840/529

Step 1: Estimating

We will have a simplified version of: 96.84/52.9, taking out 3 zeros in the numerator and 1 zero in the denominator which means that we will return 2 zeros in the last step.

Technically we need a step of “rounding” here. But in this case, we can just skip it and make an overall adjustment later.

Now turn division into multiplication and find x:

52.9 x ? = ~96.8

We know 53 x 2 = 106

Thus, ? is a little bit lower than 2.

Step 2: Adjusting

With a downward adjustment for 2, we have 1.8. And with zeros, it is 180.

The correct answer is 183.06

Hope it helps,

Best,

André

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Clara
Expert
Content Creator
replied on Jul 16, 2020
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

As detailed and agile as possible. I would practice leveraging GMAT.

GMAT unfortunately only gets better with practicing. Good news is that there are many ways of doing so!

There are free exams in the internet that you can use for practice (the one of LBS MBA page, Verits prep, as well as some free trials for courses such as the one of The Economist (https://gmat.economist.com/)

Hope it helps!

Cheers,

Clara

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Amir replied on Jun 01, 2019

Thank you everyone for your feedbacks!

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Sidi gave the best answer

Sidi

McKinsey Senior EM & BCG Consultant | Interviewer at McK & BCG for 7 years | Coached 300+ candidates secure MBB offers
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