Critical Thinking in Math Questions

Case Interview McKinsey & Company quantitative
New answer on Jul 01, 2022
7 Answers
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Anonymous A asked on Jun 30, 2022

Hi all! I am in need of some advice on math. After doing a bunch of Rocketblocks practice, I feel that I have developed a good technique for structured thinking in math questions. I develop a high-level equation, explain it to my interviewer/case partner, and then do the calculations mostly correctly. However, my biggest issue now is that I fail to think about the data points I am given. 

For example, I recently did a case about whether an oil company should build its own refinery or continue to buy from another refinery. The profitability question provided transportation costs, storage costs, price (or revenue) per gallon of oil for both options, and the initial investment cost of setting up our own refinery. I failed to realize that storage costs apply to both options and made a mistake conceptually.

How can I ensure that I do not make such mistakes when doing my math? I was told that these mistakes could harm me in the interview. Any advice would be appreciated, thank you!

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Francesco
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replied on Jun 30, 2022
#1 Coach for Sessions (4.000+) | 1.400+ 5-Star Reviews | Proven Success (➡ InterviewOffers.com) | Ex BCG | 9Y+ Coaching

Hi there,

Q: I failed to realize that storage costs apply to both options and made a mistake conceptually. How can I ensure that I do not make such mistakes when doing my math? 

I would try to clarify first the exact reason of the problem. It could be due to a variety of things:

  1. You misunderstood the objective and answer the wrong question
  2. You didn’t ask the right clarifying questions
  3. You were unable to ask for help to the interviewer when needed
  4. You didn’t do enough drills, thus you have seen a limited amount of math problems and cannot quickly identify the optimal structure
  5. You got confused by the large amount of information

Once identified the exact problem, you can drill down on a solution for it. If you want please feel free to message me and can check if I can direct you to the right process according to the issue.

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

  1. Repeat the question – sometimes candidates do mistakes answering the wrong question
  2. Ask for time and explain how you would like to proceed, presenting the formula you want to follow
  3. Perform the math and present the interim steps to keep the interviewer aligned – don’t just say the final number
  4. Continue with the calculations until you find the final answer
  5. Propose next steps based on the results you found

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Best,
Francesco

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Cristian
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replied on Jun 30, 2022
Highest recommendation rate / Top McKinsey coach / 100% success rate at >4 sessions / Honest feedback: no sugar-coating

Hi there, 

It makes sense that this is where you are currently failing. This the most difficult part of the interview - the actual interpretation and contextualization of the results - and the one that requires most practice. 

To begin with, aside from continuing practicing, what I would recommend is to take more time before answering. Try and take 50% or even 100% more time so as to think deeper about the answer you have to give. 

Best,

Cristian

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Ian
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replied on Jun 30, 2022
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Hi there,

It's pretty hard to advise you just via text here…

This requires coaching where the exact root cause of this problem is identified and worked on.

That said, it sounds like a combination of lack of case leadership and lack of business acumen.

You need to improve case leadership (tricky, best done through coaching) and you need to improve business acumen (through research, daily reading, and creating industry deep-dives).

Ultimately, across the entire case (math, exhibits, questions, etc.), you need to always be objective-driven and think “why” slash “so what”.

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Kurt
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replied on Jun 30, 2022
Conducted over 100 interviews for grads, interns & experienced hires

You are right in identifying that if you are given a data point, it almost always should play a part in your analysis. One simple check you could do is once you have set up your equation, to quickly run through the list of what you have been given and make sure there are no “unused” data points as a habit.

Your approach to lay out the equation is the right one, and it will also ensure that the interviewer can identify how you are using the information and correct you if needed. One thing you may also do to try to catch this type of mistake is to be more explicit about the assumptions you have made, and run these by the interviewer e.g. “I have assumed in option B that storage costs do not apply, have I understood this option correctly?”

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Moritz
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replied on Jun 30, 2022
Unearth your spike & get the offer |ex-McKinsey | 120+ coachings & interviews @ McKinsey | ESADE MBA | Transition Expert

Hi there,

Hard to give general advice. As for the example you give, you should have followed two steps:

  1. Verify variables: If you're working with variables for two or more scenarios, you essentially end up with a matrix. What you should be doing is systematically go through each intersection of the matrix to verify the validity and specificity of each variable. ▶ This systematic approach should prevent anything falling through the cracks and would have saved you.
  2. Set up equation: Once you're clear on the variables, you set up your equations according to the objective you're trying to solve for. ▶ It seems as though you focused on this part exclusively, which is important but not sufficient

Hope this helps! Best of luck!

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Clara
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replied on Jul 01, 2022
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

It seems to me that you are already taking the right steps to become a master in tricky math questions, congrats :)

Unfortunately, the only non-original advise that I can give you here is: practice, practice, practice. Only by doing a bunch of those you would realize mistakes like the one you point out, and don´t do them again. 

Hope it helps!

Cheers, 

Clara

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Ashwin
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updated an answer on Jun 30, 2022
Ex Manager Bain and company | INSEAD

Hi there,

It's difficult to know your precise areas of improvement without doing a mock session. However, I would suggest that before you do the math you can clarify your thinking with the interviewer and also ask logical questions to understand the business model. If you have not worked in a particular industry it's difficult to understand the business model so you can ask hypothesis-driven questions during the interview 

(edited)

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Francesco gave the best answer

Francesco

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