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How fast do I need to do math in a case interview?

Anonymous A asked on Aug 02, 2019 - 6 answers

I have an upcoming interview with BCG and am struggling most with math. I am good with writing down math and doing it but my problem is that I do not really use any shortcuts and tend to make mistakes if I am not writing everything down and doing it step-by-step. This makes it so that I take a while to do math and I feel somewhat like a primary school kid when I am writing down everything (carrying a 1/long division etc). Is it better to just do the math this way and get it right or should I take the risk of trying to do math in my head or ways that I am not used to just to go a little faster? Overall, just want to know if speed or accuracy should be compromised if I cannot deliver both which would be ideal.

In addition, also curious how much of the math I need to actually say out loud. For example, I might say, I am going to divide X by Y to get Z. Can I then be silent for a bit when I do the actual operations?

Thank you for your answers!

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Yewande
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replied on Aug 02, 2019
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First off, huge congratulations on your upcoming interview!

To answer your question direct: accuracy trumps speed: I've never said no to a candidate who ticked off all other boxes, but was slow with maths. But I have said no to a candidate who had a great case, but made so many mistakes with planning and solving the maths. (and same for other interviewers I've worked with). Think about it from a client's perspective - in the grand scheme of things, giving me a wrong recommendation because of sloppy, inaccurate maths could have a huge impact on my business, vs. you taking an extra half hour to get me a result

So... besides getting the maths right, what else will your interviewer be looking for?:

  1. You are comfortable with maths: People sometimes describe this as speed, but it's more about not being scared, sloppy, or overly confused by numbers. I want to know that you can handle numbers - big, small, decimals, multiples, divisions. And that it doesn't phase you. Recommendation: Practice mental maths to get that comfort level but when you're in the case, don't worry about speed because worry will reflect in your confidence and probably create mistakes
  2. That you can bring the client along: Remember, clients may not be comfortable with numbers. So it's not just your job to get the numbers right, but to explain what's going on. So it's less about say "I'm going to divide X by Y to get Z" and more about saying "To calculate the the difference in average price between our client and their competitor, I'm going to divide our client's total revenue (£Xm) by the number of products (Y) to get our client's average revenue. This is £Zk. And now I'm going to do the same for the competition to get £Bk. And now I'm going to subtract the difference between our client (£Zk) and competitor (£Bk) to get the average difference (£Ck). And this average difference seems [sense check / insights]. And therefore I'd lean towards [mini recommendation]". So make it real and relevant and not just about the maths.

Let me know if you have any additional questions. Have an awesome interview!

Best!

Giulia
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replied on Aug 02, 2019
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Hi,

As it often happens, I believe it is a mix of the two ;p

You always have to provide the right calculation, because if you do it wrong, they'll ask questions like "are you sure?" and you would need to compute the math once more.

I confess that it is expected that you are able to do a few maths in your head and maybe it would be better for you to exercise a bit your math abilities, before the interview.

E.g., it is generally expected that you are able to do 27/5 in your head pretty quickly (obtaining a result of "around 5,4"), while it is acceptable if you do your calculations on a paper if you are asked to do 1.547/32*4 ;p

Also, during interviews, it is acceptable to make a few rounding and I strongly encourage you to do it. E.g., 5,4 -> 5,5, 90 -> 100, and so on. Always share your thought with the interviewer, to check with them if it is acceptable for you to do such a rounding.

If your interview is tomorrow, I would go for the right results in more time than wrong results in a short time, of course.

Regarding your last question, it is always better for you to share as much of your math with the interviewer so that he/she can correct you if you are making mistakes and can follow your line of thoughts (the numbers don't have to seem popped out of your head ;p).

Thus, I would say "I'm going to divide the number of houses for the number of people, to obtain the number of houses per person. Thus, I would divide 27 million houses for 5 million people, obtaining around 5,4 houses per person, that I would like to round up at 5,5 for easiness of calculation"

Hope you'll find it useful!

Nirmit
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replied on Aug 06, 2019
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Accuracy will always trump speed

Vlad updated his answer on Aug 03, 2019
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Hi,

Here is how you can improve your math skills

Any of these tools are good: Preplounge Mental Math, V. Cheng, Mimir Math.

I recommend to concentrate on the following:

1) Learn how to multiply double digit numbers (https://www.youtube.com/watch?v=6ndkkPZYJHo).

2) Learn how to work with zeros. - always use 10^power instead of zeros

Example:

300x9000 = 3*10ˆ2 x 9*10ˆ3=3x9*10ˆ(2+3)=27*10ˆ5

Handwritten it looks not that complicated. If you get used to writing all the numbers that way, you will never loose zeros and all multiplications/divisions will be replaced with + or -.

3) Learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems

Other math skills:

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!

(edited)

Francesco replied on Aug 03, 2019
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Hi Anonymous,

it is totally fine if you write down your math. As mentioned by Giulia, sometimes the interviewer may ask to do math in your head to see how you react under pressure, but for general math in the case, writing it down is fine.

To improve your accuracy for mental math, 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 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

In terms of communication, I would recommend to explain the interviewer all the macro steps you want to follow.

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

  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 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 art fractions and thus speed up/simplify the computation - the most useful to know are 1/6, 1/7, 1/8, 1/9.

Hope this helps,

Francesco

John
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replied on Aug 02, 2019
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Hi,

some thoughts on your questions:

- Accuracy over speed - always!

- The interviewer should know what you are doing. E.g. you can tell the interviewer that you will be dividing 15000 by 25 and tell him/her the result after you are done. No need to sa: "25 into 10000 is 400 and 5000 is half of it so the result is 600"

Hope this helps.

Apart from that it is very hard to judge what is ok and what isn't from an outsider perspective. I would really need to observce you doing excercises in order to be able to benchmark you.

Best,

John

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