MATH from scartch

case math Charts MBB case interview prep
New answer on Oct 20, 2022
4 Answers
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Anonymous A asked on Oct 09, 2022

I am just starting to study how to do cases, and I didn't use math in like 6 years, my studies didn't require any math besides introductory microeconomics, macroeconomics, and statistics courses. I need to learn math super fast, and I see how it also affects me with charts. 

I CAN understand numbers, and how to use them when I have a guide of the rules and exercises to practice. 

I just don't know when to find them, and I would love it if you can advise me on the math and charts, and the quantitative aspects of the cases.

1. where can I find math practice and chart practice?

2.  Any tips on how to do it effectively and faster?

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Paul
Expert
replied on Oct 20, 2022
I love helping candidates prepare for their dream job at McKinsey

The first part of my answer deals with general Math prep. I talk about charts further down. 

Breakdown your math prep into two parts:

  1. Mental arithmetic: The actual crunching of numbers. There isn't anyway around this other than practice but luckily its easy to do. You can practice by downloading any one of the many different apps that throw simple multiplication and division problems at you, and spending 10 - 15 minutes a day on it. Its amazing how quickly your 12x table comes back, and it's important to feel confident when doing simple calculations - you want to know that when have to crunch the numbers, you can execute fairly quickly and accurately.
  2. Setting up the problem you are trying to solve. By this I mean clarifying what you are trying to calculate and then setting up the equation you need to solve. Most people are nervous in the interview and probably nervous about the math question too, so as soon they hear a math problem they panic and immediately start trying to crunch numbers. It is amazing how many interviewees cannot recall the question they are trying to solve. As an interviewer, time and time again I would stop a flustered candidate who was getting tangled up in the math and ask them if they could remember what they were trying to calculate and almost always they could not remember. 

Here is a good step by step process for answering the math question:

  • Clarify out loud EXACTLY what you have been asked to solve
  • Tell the interviewer that you are going to take moment to consider your approach
  • PUT ALL NUMBERS ASIDE and write down in words the equations you need to solve. This has several advantages: 
    • a) if you structured the problem correctly will already have been given most of the credit just for knowing what to do
    • b) you will make it easy for the interviewer to correct you early on if they can see you are on the wrong track and where you are going wrong (it is very frustrating for an interviewer who is waiting for a candidate battling away in their head trying to work out an answer. The interviewer can't see where they are going wrong and thus finds it hard to help them. Trust me, if a candidate is on the wrong track, the interviewer wants to help them - but its much better if the candidate makes it easy to help them!
  • Never attempt to manipulate more than 2 numbers at once. The risk of making a mistake far outweighs any small benefit you might get from impressing the interview with your amazing mental arithmetic. For example if you need to calculate  X * Y + Z, work out X*Y and write down the answer before you continue. Again, its making it easy for the interview help you if you make a mistake
  • Don't forget to interpret your answer. Consultants never just do math for fun. The point is to get an answer that moves the case forward. Most candidates are so relieved to have reached the correct answer that they forget it is actually part of a broader case - all you need to do is make a comment or two about what the answer means

The above is a good approach but I can almost guarantee that if you don't practice that approach you will almost certainly forget one or more of those steps when answering a math question.

Getting comfortable with charts

Usually in a McK interview you will be handed a chart and asked to interpret it. For interpreting charts, I advise talking out loud from the beginning and explaining what you see, starting with the most obvious points and working towards more insightful observations. This approach has a several advantages:

  • It avoids a long silence as you try to formulate a perfect answer in your head
  • It prevents silly mistakes caused by assuming what the chart is about rather than reading what it actually says
  • It allows the interviewer to correct you early on if you do misunderstand something 
  • It ensures your answer is comprehensive. Many interviewees fee shy to state what they consider obvious facts but this leaves the interviewer having to guess whether or not they actually noticed the obvious facts at all. 

So to practice - get a bunch of charts from old cases then do the following:

  1. Read the title of the chart out loud (e.g. Revenue of major competitors in XYZ industry)
  2. Tell the interview what data the chart is presenting including units (e.g. Okay, I see on the y-axis we are being given revenue in M USD, and on the x-axis we have the 10 largest competitors. For each competitor we are given annual revenue over the last 3 years
  3. Start to make simple observations. For example - I see that the 2 largest competitors are much bigger than all the others, in fact they are both larger than the next 8 combined
  4. Make more detailed observations (usually some sort of change that the chart is indicating). For example - "going back 3 years the market was much more competitive, so there has been some consolidation in the market. The largest competitor today was not even in the top 5 just 3 years ago. They have more than doubled their revenues"
  5. Set your self apart by pushing to make 2 or 3 really insightful observations that are usually informed by more than 2 pieces of information contained within the chart. At this point you are speculating and forming hypotheses so you should also acknowledge the limitations of the conclusions that you are drawing and mentioned that more information would be required (but now you now what to look for).
  6. Bring your answer to a professional close. Most candidates I ask to interpret a chart talk for a while then sort of trail off and give me a questioning look to see whether they have said enough or whether they should carry on. Once you have finished interpreting the chart you can summarize your answer then just stop talking and it will be clear to the interviewer that you have finished talking. For example say something like - "So to recap; I can see from chart that this market is highly consolidated with the 2 largest players accounting for more than 80% of the revenue. This was not the case 3 years ago so when the industry was much more competitive. Based on total revenues of the top 10 companies over the past 3 years, it looks like the industry is growing, but the two largest (Company X and Company Y) are also growing at the expense of some of their competitors. There appears to have been some change in the industry a few years ago - we don't know what this was, it could have been regulatory or technological but we would need more information to answer that."

Again, the above approach sounds simple but it takes practice to internalise the process. Once you have the process sorted you will look forward to being handed a chart to interpret

Best of luck!

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Mario
Expert
replied on Oct 09, 2022
Ex-Mckinsey (analyst->associate->manager) and now in tech (Bytedance) + Part time interview coach and mentor

Hi there,

 

I recommend practicing quant questions from actual case studies, as opposed to just practicing math in silo. 
 

As for the tips, below are a few:

A- Round your numbers

Whenever you can, ask whether the interviewer is okay with rounded answers. You can frame it as ‘should I get the exact figure or can I take proxies". You’ll be surprised to see that many (not all) will be okay with proxies as they are really testing your structure. In some cases, they'll still ask for the exact figure though.

 

B- Reordering

The order in which you solve an equation matters a lot. Starting with the wrong pair might complicate things a lot (e.g. get you into decimals)

 

C-  Replacing zeros with symbols

Use K, M, B as opposed to tens of zeros. That leaves you with a max of 3 digits to worry about. e.g., 10,000x25,000 is 10kx25k which is 10x25M which is 250M

 

D- Decompose 

It's sometimes helpful to decompose some complex figures into easier ones and tackle then in 2 shots vs 1 only e.g., decomposing into sums or fractions

 

Can give you more tips as needed !

 

 

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Ian
Expert
Content Creator
replied on Oct 09, 2022
MBB | 100% personal interview success rate (8/8) and 95% candidate success rate | Personalized interview prep

Hi there,

Most casebooks have a section on math...but I wouldn't rely on this for your prep.

  1. 100% Recommend Rocket Blocks. 
  2. Math sheets from Math Drills Website
  3. In addition to that, you can ask other PrepLoungers to case you on math-heavy cases. You can also search for those case types here and work through them yourself.

Some key formulas/concepts:

  • Breakeven
  • NPV (with + without growth, perpituity + 1-2 years from now)
  • % Change
  • ROI
  • Margin
  • Markup
  • Inventory turnover

----------------------------------------------------------------------------------

Some great answers from a variety of angles have already been asked. Check these out!

Mental Math

https://www.preplounge.com/en/consulting-forum/mental-math-help-7962

https://www.preplounge.com/en/consulting-forum/is-quick-mental-math-a-skill-that-can-be-learned-5210

Conceptual/Contextual Math

https://www.preplounge.com/en/consulting-forum/materials-for-practicing-conceptual-case-math-8016

https://www.preplounge.com/en/consulting-forum/math-concepts-6951

Key Math Equations

https://www.preplounge.com/en/consulting-forum/math-equations-their-use-7934

Math Practice

https://www.preplounge.com/en/consulting-forum/case-math-practice-6877

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Lucie
Expert
Content Creator
replied on Oct 10, 2022
10+yrs recruiting & top BCG trainer & BCG Project leader & experienced hire & ICF coach

Hi there, 


From my point of view and experience of my coachees I would recommend:

1. Read a few books on math shortcuts and tips (Speed mathematics, Tricks to become Human Calculator)


2. Check videos on youtube explaining shortcuts 


3. Eventually take a course (the one that seems good is GMAT | Quantitative | Master Math Course etc.)


4. Last option which I think is probably the best is to get a math tutor (not a coach here), someone who helps students at schools (probably the best value for money).


5. On top of a lot of training and drilling


The good thing is that math can improve fast with exercising. 


Good luck
Lucie
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Paul

I love helping candidates prepare for their dream job at McKinsey
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