All questions tagged math - Consulting Q&A - PrepLounge.com

Hello!

For what I have seen with my coachees, people struggle the most when calculations are "long" (i.e., many chained calculations in which the end you loose magnitude of numbers). This could be the case with, for instance, market sizings.

In these cases, it´s key to break down into little pieces, and solve one by one, instead of attaching the whole operation at once.

Cheers,

Clara

Hi,

I recommend downloading all casebooks available online and check the math problems. You'll have a good list. Here are some of them to keep in mind:

• Interest rates calculations
• Compound margin
• NPV using the Rule of 72, Perpetuity
• 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 (Integrals)
• Profit / breakeven formula
• Correlations, outliers (being able to spot on the graphs, tables)

Best

Hello!

Bear in mind that approximations are not only "accepted", but also a good sign (e.g., I prefer a candidate who gives me the "good big numbers" in a very agile way that one that takes long to give me the exact number)

In this case:

• 0.55 can be rounded to 0.5
• Dividing by 0.5 is the same as multiplying x 2
• 340 x 2 can be broken down into:
  • 300x2 = 600
  • 40 x 2 = 80
  • 600 + 80 = 680
• At this point, you can even realize that, since you divided by 0.5 instead of 0.55, your number should be smaller (by approx 10%, so you can approximate to 620 for simplicity of further calculations -the accurate number would be 618.18-.

Hope it helps!

Cheers,

Clara

Hello!

The best is to practice, practice, practice! I could recommend you to start with:

1. GMAT exams: that can be found for free in the internet (GMAT prep with The Economist, London Business School free trial, etc.)

2. Math tools: such as Mimir math for iOS or Math tool on Viktor Cheng´s website)

3. Multiplying any two 2 digit number in 3 seconds: check this great video > https://www.youtube.com/watch?v=6ndkkPZYJHo

Best,

Clara

Hi Anonymous,

as general practice for the PST, I would recommend the following approach:

1. Try to find at least 5-6 practice cases online. There are several available for free, if needed you can purchase additional ones.
2. Do one of the tests immediately to check your score. As the passing score is around 70% and you have 26 questions, your target score should be above 18 (keep in mind you are likely to score a bit less in the actual test than your average score at home due to time pressure/nervousness). In the first test you are likely to score lower than that - don't worry, that's pretty normal.
3. Identify the type of questions where you made more mistakes. There could be different reasons why you are doing mistakes and there is probably a predominant type of mistake you are doing (eg slow math or weak critical reasoning). You have to identify the reasons for the mistakes and a way to fix them.
4. Continue the preparation with the remaining tests. After you have identified the main reason for mistakes, you can continue the preparation with the other tests before the interview - I would allocate them at a regular time distance, with an increase in frequency closer to the day of the test.
5. Go again through the questions where you did mistakes at regular intervals. Be sure to keep a "failure" spreadsheet, where you report all the mistakes and classify the reason for them each time.

The key areas where you may do mistakes and may need to practice are the following:

1. Time management. Commit to an amount of time for each question, and go on if you surpass that time. If you do not set discipline, you will end dedicating too much time to some questions (these tests are sometimes structured with questions that are supposed to be skipped and reviewed at the end). If time and test allow, you can then go back to the questions at the end.
2. Quick math. I would recommend practicing with online tools on a daily base to improve. It is better to allocate a small amount of time daily rather than to practice intensively few days only before the interview
3. Quick reading. Get a Harvard Business School case or an equivalent long one, give yourself 2 minutes and check how much information you can absorb. Then repeat until you get a sufficient level of accuracy. You can also check speed reading tactics (eg Tim Ferriss ones) and see if they work for you.
4. Graph interpretation. You need to practice on how to derive quickly insides from graphs. Take some random graphs, give yourself 30 seconds and check if you can get the main insides from them. Then repeat until when you get a sufficient level of accuracy
5. Critical reasoning. The GMAT critical reasoning section should be a good support as practice

Hope this helps,

Francesco

Hi,

Here is a set of things you need to know:

1) Math and formulas:

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

2) Fast math skills

• Rounding up and down
• 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 using powers (e.g.: 4000000 = 4*10ˆ6)

Use math tools (Mimir math for iOS), Math tool on Viktor Cheng website to practice

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)

Good luck!

Hi,

Something that helped my candidates - download ALL casebooks available online and go through the math problems in the cases. They will give a good sense of required business terminology. Then you can google what you don't know.

P.S. don't follow the books solutions to solving the cases since they are not that good. Just practice the math problems

Best

Hi,

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

It's more about the skills. 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. You've mentioned - 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

Good luck!

Hi,

Simply learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems. For example, if your market is $620M and your revenues are $51M you can use 5/6 as a proxy to calculate the market share

Best!

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!

Hi,

Basically, you need to develop 3 calculation skills:

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

2) Learn how to work with zeros. Best way - 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. For example, if your market is $620M and your revenues are $51M you can use 5/6 as a proxy to calculate the market share

Good luck!

Hi!

Here are my 5 tips:

1) Practice mental calculation daily (percentages, decimal places, large numbers, arithmetic) – even though it's not the most important part of the interview and it's allowed to make mistakes, you need to master your numbers very comfortably. If you don't, during the interview you will start feeling nervous and will perform worse on other things. I was doing at least 30 min a day of mental arithmetic for several months (download one of the apps on your phone, there are plenty).

2) Cases, cases, cases – do as many as you can. After you gather a bit of experience of practicing with your fellow students, try to find a person who is now working or has worked in the past at the MBB's recruting and ask them to simulate an interview with you.

3) Prepare and practice personal fit interviews – they are as important as the cases. Write down your stories, practice telling them with your fellow students, or with an expert.

4) Beware of your mental state – try not to stress too much before and during the interview (I know it's easier said than done). Do sports, take care of your health, try yoga, meditation – whatever makes you less stressed. I've seen so many candidates pale as a sheet of paper during my time as an interviewer at McKinsey, all worried and jittery – as you can imagine this doesn't help your performance.

5) If you get rejected, it's not the end of the world, do prepare yourself mentally for this thought! A close friend of mine became depressed for months after being rejected at McKinsey. I think it was because she treated this as a "do or die" situation. Do not do that! There are infinite options of different careers and adventures out there, you don't need to become a strategy consultant to be happy. Just try to embrace this before going into the interview room – and you will be better prepared for both failure and success.

Hello Sabrina,

I would recommend you three things:

1. Write all standard formulas together (break-even, NPV, etc) and memorize them. With that a large part is already won!
2. For developing unknown formulas in the case situation, you can practice with math exercise books (it is a mixture of solving equations and text exercises in math).
3. If you have issues with mental arithmetic, you can practice very well here: https://www.preplounge.com/de/mental-math.php

Best regards
Marco-Alexander

Hi Anonym A,

for many who have difficulty with mental arithmetic, it's just the stressful interview situation. What about you? How good are you at mental arithmetic if you practice alone at home?

If it's just nervousness, I would recommend you practice the interview situation as often as possible (e.g. with friends or on Preplounge).

If it's the mental arithmetic itself, you can practice very well here: https://www.preplounge.com/de/mental-math.php
If there is no other way, you can also do the calculations in writing on paper. However, I wouldn't advise you to memorize any multiplication tables.

If you have further questions, please contact me!

Best regards
Marco-Alexander

Hi,

I'm afraid the best and the only way is to download all casebooks available online and go through the math problems in the cases. Several formulas and tools can be useful:

• 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)

Best!

Hi Anonymous,

the market, the company, the customer preferences etc. all play into the financials. The financials are DRIVEN by these factors! So you need to outline the numerical driver tree, and then connect the aforementioned factors to the metrics and sub-metrics in your tree. Then in analyzing, you need to examine the market, customer preferences etc. in order to derive the financials.

Cheers, Sidi

Hi,

When performing a calculation, I recommand :

• Split the discussion in two : start with the structure of the calculation, and once it's validated draw hypothesis and perform the calculation
• when perofrming the calculation, we don' t expect you to be supper fast, be at least to be accurate. So in case, it's super direct, you should ALWAYS write down on the paper the calculation. I also recommand to proceed with intermediate steps in the calculation so it will be easier to correct in case there is a mistake.

Best
Benjamin

You're correct in stating that the assumption of "court use = 1 hour per member per week" means that each member can only use the court for one hour per week. This prevents double counting as each member can only use a court once per week.

In terms of the implicit assumption, in a case interview context, you would want to make that an explicit assumption. If you didn't do this, you may calculate the wrong number due to an incorrect assumption. For example, you could say "Can I assume that only members can use the courts, and they cannot invite friends?". The interviewer would then say yes or no which you would then incorporate into your analysis.

Hi,

Pls find below my list

1) 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, Perpetuity
• CAGR using the Rule of 72
• Currencies exchange calculations
• Speed, time, distance calculations
• Equations, systems of equations
• Ratio & Proportions
• Little's Law
• Solving the problems by calculating the area of the triangle
• Profit / breakeven formula

2) Fast 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 Preplounge 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)

Good luck with your interviews!

Whatever works best for you - your notes are non-evaluative (except in the context of communicating your structure) and will be thrown away after your interview. Therefore the only consideration is what helps you.

Personally, I found graph paper helpful for math and for structuring neatly.