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Resources / approaches to improve "case math"?

Math problem
New answer on Aug 31, 2023
8 Answers
538 Views
Anonymous A asked on Jul 25, 2023

Hi, I'd like to seek your advice on how to develop “number sensitivity” and solve case maths effectively? I sometimes get stuck at cases with more complicated math, and fail to come up with a calculation approach effectively. I'm thinking how to 1) become faster in coming up with the approach & math equation 2) structuring a math solution that could solve the client issue effectively and with more insight

In this case, except practicing brain math, market sizing, and practicing math problems of the cases that I've done, are there anyways to systematically enhance this improvement area? What would be the most efficient approach?

Thank you!

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Sophia
Expert
replied on Jul 26, 2023
Top-Ranked Coach on PrepLounge for 3 years| 6+ years of coaching

Hello,

Looks like you've gotten some great advice on systems and breakdowns on how to improve case math, so here's my additional two cents:

First, remember that practice makes perfect! If you are at the initial stages of case interview prep, it's perfectly normal that case math questions seem a bit unnatural and confusing. You will likely see yourself improve naturally over time as you practice more cases and get the hang of the math a bit more.

If you're somewhat advanced into your case prep journey, I would recommend the following. Do some drills with math questions by taking cases, listening to the prompt, skipping the framework and qualitative questions (or skimming them so you get context), and then get really work on the math part. I would get out of interview mode, give yourself time, and practice some of the step-by-step processes provided by coaches here. Don't worry about doing it too quickly, at first make sure you have a good approach in place. Another suggestion is to go back and review the math questions on cases you've done.

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Benjamin
Expert
Content Creator
replied on Jul 26, 2023
Ex-BCG Principal | 8+ years consulting experience in SEA | BCG top interviewer & top performer

Hi there,

I'll share from my own experience improving my math. Math and quant was never one of my strong points - I couldnt even pass pre-university math, and to top that off I studied History in college, so trust me when I say that math was something I feared back then when I was preparing for my interviews :)

There are already great suggestions by other coaches on how to approach math during the case. I'll give a perspective on your question on how to systematically enhance this improvement area. 

  • Market sizing and mental math help - but those are just the ability to do the calculation
  • On the job - excel/alteryx will do the calculation for us, and MBB is not hired to do calculations. Often, the logic is the far more important point
  • What worked for me was to start forcing myself to think and reason quantitatively in as many scenarios as possible in life, and come up with ‘formulas’ to try and get to a quantitative answer or solution to a situation or problem or question
    • E.g. if I was deciding which credit card to sign up for, how would I quantify this decision? e.g. maybe considering cost of annual fees, upside of redemption points etc
    • E.g. if I was deciding between going MBA versus staying in my job, how would I decide on this quantitatively? 
    • E.g. you are facing a long queue at the supermarket - ask yourself a hypothethical question of how many additional counters would be needed to reduce the queue/waiting time by [50%]
  • While of course many calculations on the job will be about revenue & cost, I've had my fair share of calculations that did not involve $$ (not immediately) and were sometimes fairly ambiguous
    • E.g. for a strategy project, I once had to estimate/calculate the number of doctors it would require to adequately serve a new telemedicine channel
    • E.g. for a diligence, I once had to estimate/calculate how many delivery riders were needed to deliver parcels on time within a certain time limit and delivery radius
    • E.g. for a diligence, I once had to estimate/calculate whether advertising on YouTube would be more lucrative than advertising on another media platform

All the best!

 

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Carolin
Expert
replied on Jul 25, 2023
1st meeting -50% | BCG | 15+ MBB offers secured for coachees | Empathic & enthusiastic coach

Hi!

I would approach this the following way:

1. Ask yourself during the case: Do I need a precise answer to the last digit, or is a rough ballpark estimation enough? You will have a feeling based on the case and the question that the interviewer asks. For example, market size questions do not need to be super precise, whereas calculating gross margins across product lines should be precise.

2. If a precise answer is required, you can still ask if rounding is okay. The interviewer will tell you without any hard feelings.

3. Take some time to structure your calculation. You can even tell the interviewer, "I will think about how to solve this problem in the most efficient manner possible for a minute." Then, write down your math approach and walk your interviewer through your math structure before doing the actual calculation. This will help you validate your approach and also guide the interviewer through your thinking (without the actual numbers).

4. During the actual calculation, again, do not rush! Write the calculation down and believe in yourself! Make a logical sense check, for example, check if the comma is in the right place.

5. Lastly, always ask yourself after you have done a calculation: What does this mean? Is the number big or small? Does this validate or contradict my hypothesis?

I believe that you will become faster with practicing different cases. Hope this helps!

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Cristian
Expert
Content Creator
replied on Jul 26, 2023
#1 rated MBB & McKinsey Coach

Hi there!

Yes, there is. 

Basically, you need to break down the calculation into steps and build buffers of thinking time for each of them. 

The whole point of this is to make sure that you can give the best, most insightful answer AND connect with the interviewer at the same time. 

Step 1. Validate the data and question.

Make sure that you understood what is being asked of you. 

If you are unsure about any of the data provided, play it back to the interviewer to check it. 

If you have any exhibit, read it with the interivewer and ask clarifying questions (if applicable).

Step 2. End-to-end and step-by-step logic.

Now take time and on your own try to come up with an end to end and step by step approach to solving the problem. 

Then present it to the interview. 

The key is not to bring the numbers in at this point. 

Use it as an opportunity to discuss and CO-CREATE the logic with the interviewer. 

Once the interiewer agrees with the logic, then you can move to the next step. 

If they don't agree with the logic, adjust the approach until you are aligned. Same as you'd do with a client. 

Step 3. Do the computations

Take the time to do the computations on your own. 

Validate and sanity check them. 

Then get back to the interviewer and take them through the same steps as in the calculation question but now with numbers attached to them. 

Until they confirm that the number you arrived at is correct. 

Step 4. Interpret the result. 

Once they confirmed the number, provide an interpretation for the result. 

Seek not only to answer the question you were given but also to contextualise the answer within the situation of the client. 

i.e., what should the client do as a consequence of your findings

Hope all of this helps!

Feel free to also reach out for the full guide for free.

Best,
Cristian

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Francesco
Expert
Content Creator
replied on Jul 26, 2023
#1 Coach for Sessions (4.500+) | 1.500+ 5-Star Reviews | Proven Success (➡ interviewoffers.com) | Ex BCG | 10Y+ Coaching

Hi there,

Q: I'm thinking how to 1) become faster in coming up with the approach & math equation 2) structuring a math solution that could solve the client issue effectively

It seems your issue is mainly on how to structure the math equation. 

To fix this, I would try to identify the math questions for which you have more problems. Most likely you are fine with many but there might be specific areas where you struggle (eg breakeven or capacity issue).

Once identified them, I would try to do drills/review the approach specifically for those questions. This should make your preparation more efficient compared to doing general math practice.

As general tips for math, I would recommend the following:

  1. Repeat the question – sometimes candidates do mistakes answering the wrong question. 
  2. Ask for time and present how you would like to proceed from a theoretical point of view
  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 math until you find the final answer
  5. Propose next steps based on the results you found

Hope this helps,

Francesco

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Ian
Expert
Content Creator
replied on Jul 26, 2023
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi there,

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

  1. 100% Recommend Rocket Blocks. https://www.rocketblocks.me/
  2. Online "Drills": https://www.jetpunk.com/quizzes/fast-math-multiplication-quiz
  3. Math sheets (print these and do them on paper): https://www.math-drills.com/
  4. 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

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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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Clara
Expert
Content Creator
replied on Aug 31, 2023
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

Precisely for the high amount of questions (1) asked by my coachees and students and (2) present in this Q&A, I created the “Economic and Financial concepts for MBB interviews”, recently published in PrepLounge’s shop (https://www.preplounge.com/en/shop/prep-guide/economic_and_financial_concepts_for_mbb_interviews).

After +5 years of candidate coaching and university teaching, and after having seen hundreds of cases, I realized that the economic-related knowledge needed to master case interviews is not much, and not complex. However, you need to know where to focus! Hence, I created the guide that I wish I could have had, summarizing the most important economic and financial concepts needed to solve consulting cases, combining key concepts theorical reviews and a hands-on methodology with examples and ad-hoc practice cases.

It focuses on 4 core topics, divided in chapters (each of them ranked in scale of importance, to help you maximize your time in short preparations):

·        Economic concepts: Profitability equation, Break even, Valuation methods (economic, market and asset), Payback period, NPV and IRR, + 3 practice cases to put it all together in a practical way.

·        Financial concepts: Balance sheet, Income statement/P&L and Performance ratios (based on sales and based on investment), +1 practice case

·        Market structure & pricing: Market types, Perfect competition markets (demand and supply), Willingness to pay, Pricing approaches, Market segmentation and Price elasticity of demand, +1 practice case

·        Marketing and Customer Acquisition: Sales funnel, Key marketing metrics (CAC and CLV) and Churn, +1 practice case

Feel free to PM me for disccount codes for the guide, and I hope it helps you rock your interviews!

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Andi
Expert
replied on Aug 31, 2023
BCG 1st & Final Round interviewer | Personalized prep with >95% success rate | 7yrs coaching | #1 for Experienced Hires

Hi there

adding some thoughts to the great advice already given by other coaches..

  • Drill drill drill to make sure your actual computations become second nature don't consume too much mind space. That way you'll have more capacity to actually think through the problem conceptually. Arithmetics, % Maths and simple algebra is are usually all it takes.
  • Experience helps - similar to the above, the more scenarios / problems you have seen, the more pattern recognition will help you tackle complex Maths parts more effectively and efficiently 
  • Practice real case maths examples once your foundations are solid. MBA case books are a great, free source for that. Going through the Maths problems in those will give you very relevant exposure.

Hope this helps.

Regards, Andi

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Sophia gave the best answer

Sophia

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