How can I improve at consulting math?

case math consulting Math problem
New answer on Jul 17, 2020
6 Answers
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Anonymous A asked on Aug 04, 2019

Hello Everyone, my question is regarding chiseling my math skills. Often in number instensive cases we are required to do math involving complex numbers relatively fast. Is there any way I can work on this apart from consistent pratcice? If anone of you could link me up to any tips and tricks you follow or any resources I could use to prepare, that would be great.

Thankyou!

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Francesco
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Content Creator
updated an answer on Jun 16, 2020
#1 Expert for Coaching Sessions (3.700+) | 1.300+ Reviews with 100% Recommendation Rate | Ex BCG | 8+ Years of Coaching

Hi Anonymous,

in terms of how to approach math in the case, this is what I would recommend:

  1. Repeat the question – candidates sometimes do mistakes answering the wrong question in the math part
  2. Present how you would like to proceed from a theoretical point of view (you may ask for time before presenting if you initially don't know how to approach the problem)
  3. Ask for time and perform the first computations
  4. Present the interviewer interim steps to keep him/her aligned – don’t just say the final number
  5. Continue with the computations until you find the final answer
  6. Propose next steps on the basis of the results you found

In terms of general math tips, this is what I would recommend:

  1. Use correctly 10^ powers in your math computation. For example 3.2B/723M can be transformed in 3200*10^6/732*10^6, which makes it easier to deal with math
  2. Ask if it is fine to approximate. When you have to deal with math in market sizing, and sometimes even in business cases, you are allowed to approximate math to simplify the computation. In the previous example, for instance, you could transform the computation in 320*10^7/73*10^7, making the overall computation faster.
  3. Keep good notes. One of the reasons people do mistakes with big numbers is that they don't keep their notes in order, thus forget/misreport numbers
  4. Divide complex math in smaller logical steps. This is something you can use for big numbers after the application of the 10^ power mentioned above. If you have to compute (96*39)*10^6, you can divide the first element in 96*40 - 96*1 = 100*40 - 4*40 - 96*1 = 4000 – 160 – 100 + 4 = 3744*10^6
  5. Use shortcuts for fractions. You can learn by heart fractions and thus speed up/simplify the computation - the most useful to know are 1/6, 1/7, 1/8, 1/9.

Finally, in terms of practice before the interview I would recommend to practice math under pressure - not just math. Many candidates are totally fine with calculating 67% of 67 in a quiet environment, but freeze if you ask this suddenly in a case interview.

To practice for this, try always to use a timer with a strict time constraint when you practice math – this will create pressure and help to replicate the actual environment of the interview.

Hope this helps,

Francesco

(edited)

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Anonymous replied on Aug 04, 2019

Hi,

The best way is to practice, but practice in a smart way. Here are some tips and tricks to be most effective:

  1. Practice in front of someone else. I see loads of candidates say they have practised their maths, but when it comes to doing it infront of me, they fall apart due to lack of confidence or because they can't explain their work and do the maths at the same time. It is not enough to just practice maths, but to get comfortable doing it in front of other people
  2. Practice in real life to gain muscle memory. Instead of just doing maths to solve your cases, make it a regular part of your ongoing mental capacity by practicing in all situations. Here are some in-real-life things you can do:
    1. Do mental maths when buying groceries - this is a great way of practising estimating, multiplication (when buying multiple items), and keeping track of numbers. To keep you comfortable with numbers
    2. Do some maths when reading business reports. If an article gives you some numbers, e.g. increase in a country's GDP by x%, go ahead and work that out yourself. And then figure out what that means to the point the article is trying to make
    3. Use online mental math tools. This is the one I used, but there are likely others: https://www.caseinterview.com/math/home.php

All the best! And let me know if I can help with anything else.

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Sadik
Expert
replied on Aug 04, 2019
Ex M&A banker and Consultant at JP Morgan and Oliver Wyman

It seems the other experts have already provided the key insights!

There are a few books out there that can support you as well in terms of learning quick math such as Fast Math: Learn the Secrets of Mental Math

My key suggestion on mental math during an interview is to be ready to do all out loud. Especially if there is a lot of calculations make sure you walk the interviewer through your calculations out loud. So that he can follow it and hear how you think.

In addition, if you ever have strange number sanity check your results. If you can find your own mistakes it gives a lot of comfort to the interviewer.

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Anonymous replied on Jul 17, 2020

Dear A,

I have some thoughts and recommendations regarding your question:

• For practicing and improving your mental math you can find also some apps and tools, besides Victor Cheng’s math tool (Magoosh's mental maths app, Mental math cards challenge app etc). But there are some facts that will help in overall improvements:

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.

• The time pressure in case interviews is severe and you cannot afford to waste time. But to make your calculations right you shouldn’t be in a rush. So, I would recommend you here to work on both - practice with time limitations and learn how to keep your mind peaceful and concentrated (it might be not so popular advice here, but mediations really make their job here).

•The next important thing is that rather make it on the paper to structure the notes and then to communicate the results clearly rather than make your calculations fast

• Be comfortable and confident to state your answers not as a questions. Interviewers notice this, and this will not give a credit.

If you need any further help or career advice, feel free to reach me out.

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!

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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Vlad
Expert
Content Creator
replied on Aug 04, 2019
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School

Hi,

Here is how you can improve your math skills:

1) Mental math - train, train, and train again

  • Learn how to multiply double digit numbers (https://www.youtube.com/watch?v=6ndkkPZYJHo)
  • Learn the division table up to 1/11 (i.e. 5/6 = 83.3)
  • Learn how to work with zeros (Hint: 4000000 = 4*10ˆ6)
  • Use math tools (Mimir math for iOS), Math tool on Viktor Cheng website to practice

2) Critical Reasoning (for PST)

  • GMAT test CR and IR parts (Official guide and Manhattan prep)
  • Mckinsey practice tests
  • PST like tests from the web

3) Working with tables and graphs and deriving conclusions

  • Study "Say it with Charts" book
  • Check all available MBB presentations and publications. Practice to derive conclusions and check yourself with the actual ones from the article/presentation
  • GMAT IR part (Official guide and Manhattan prep)
  • Learn basic statistics (Any GMAT or MBA prep guides)

4) Case math

Practice common market sizing topics (Airport passenger flow, real estate volumes, subway passenger flows, car usage, etc.). You should become comfortable with making assumptions

Learn key financial topics (P&L and balance sheet and how to analyze them, Basic Valuation principles via NPV and comps) and case math:

  • Interest rates calculations
  • Compound margin
  • NPV using the Rule of 72, Perperuity
  • CAGR using the Rule of 72
  • Currencies exchange calculations
  • Speed, time, distance calculations
  • Equations, systems of equations
  • Ratio & Proportions
  • Solving the problems by calculating the area of the triangle
  • Profit / breakeven formula
  • Correlations, outliers (being able to spot on the graphs, tables)

Good luck with your interviews!

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Francesco gave the best answer

Francesco

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