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

Hi there,

Some key formulas/concepts:

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

Some other helpful Q&As:

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

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

Hello!

GMAT & the similar tests (like this one you are referring to with LEK), unfortunately only gets better with practicing. Good news is that there are many ways of doing so!

There are free exams in the internet that you can use for practice (the one of LBS MBA page, Verits prep, as well as some free trials for courses such as the one of The Economist (https://gmat.economist.com/)

Hope it helps!

Cheers,

Clara

My understanding is you should not have to worry about geometry and trig. Much more important are equations/math that have to do with key business terms incl breakeven, margins, ROI, NPV, etc. etc.

In general, the best way to prepare is to find online tests / questions and practice. Regardless as to whether is a new or old test, the principles are mostly the same:

• Time management (need to think quick)
• Business knowledge/context (incl key formulas)
• Critical thinking (answers that are very similar to each other...clues "hidden" in the text)
• Ability to interpret data/charts

Think of it as a merge of a case and the GMAT/GRE.

You need to be clear on some key case-related and account formulas (margin, growth, breakeven, etc) as well as be good at critically understanding the question (including nuance to questions) and parsing through complicated text with a fair amount of distraction.

You'll also need to be good at chart/graph reading.

The (old) McKinsey PST, BCG Online Test, Bain SOVA test, etc. are all quite similar so leverage resources across all of them.

https://www.myconsultingoffer.org/case-study-interview-prep/bcg-online/

https://www.shl.com/shldirect/en/practice-tests

https://www.psychometricinstitute.co.uk/Free-Aptitude-Tests.asp

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,

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!

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,

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!

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!

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 Richard,

Thanks for sharing! Actually I have many candidates that struggle with mental math, I will take a look to your app.

Best,
Luca

Hello!

This is indeed a great point to flag, since it´s one of the things that got more complicated with the online version of the loops.

Indeed, "guiding your interviewer through your toughts" is always a classic in coaching sessions.

There are indeed many techniques that you can leverage to improve:

• Never doing the calculations on your own and only communicating result. Instead, commenting every point out loud, to ensure the interviewer follows every step
• Problem-solving with the interviewer, precisely as you would do with your client (e.g., atm, we have calculated a total cost of 5MM €, is this a number with which the client, given his/her industry knowledge, would be comfortable?)

Hope it helps!

Best,

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

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 Sabrina,

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

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, I would recommend the following:

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

Finally, in terms of formulas, this is what I would recommend:

1. Write down all the new formulas/concepts you find when practicing cases
2. Learn the formulas
3. Look for quant parts in casebooks searching for the keywords interesting for you (eg DCF) to see possible applications for the most challenging ones

I would also 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.

In order to do so, 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.

Hope this helps,

Francesco

Math in college is not the same as math when given in a case. The main difference being that case math requires understanding of context. This context is given in verbal form which you then have to interpret into an equation and solve accordingly.

This is why the best way to practice these problems is to use a GMAT type of book. Maybe read aloud the questions to yourself and then answer them. Once you get better at these then move on to real cases to further improve.

All the best,

Udayan

Hi,

There are 2 types of BCG tests:

1. GMAT-like test with questions similar to GMAT
2. Online Test that is based on a case and has the questions closer to PST

I have uploaded both test samples here (Online test is about airlines). I've also added BCG written case sample (Next round) and Bain written case:

https://www.dropbox.com/sh/zor4m49eyx5qxal/AABeUN6mtiGkWhEklRjszX2Oa?dl=0

As for particular recommendations for online test:

1. Try to find as many people in your country as you can who have done the test. Ask them for the topic, industry, and questions they remember. For example in one of the countries there was a test about airlines and reading a couple of articles / company reports / wikipedia articles with industry terms could significantly improve performance
2. Try to practice tests with strict time-management. McKinsey PST from the official web site and all mck and bcg -like tests you can find online
3. Additional resources can be GMAT Integrated reasoning from the official guides and apps if you feel that you are not p[erforming well
4. As far as I remember calculator is allowed on BCG test. Make sure you know how to simplify calculations and use it fast

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

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