Hi all - does anyone have any material to prep mental maths? Thanks a lot!

Case Calculations case interview preparation case math Division Math problem maths McKinsey mental math New Online Tests
New answer on Nov 10, 2020
29 Answers
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Anonymous asked on Jan 19, 2018

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Originally answered question:

Any tips to do math calculations fast ?

Nabil (Bill) replied on Jan 16, 2017
Currently preparing for McKinsey and Bain interviews.

In order to perform math calculations faster, here are some tips you can use:

  • Increase the number of steps in your calculations and turning complex operations into simple ones: It seems counter-intuitive but let me explain. Let's consider the following example: 67 x 89. If we were to calculate this the traditional way, then we would waste considerable time which will have a negative impact on our overall performance during the interview. Instead, by increasing the number of steps in the calculations, we can bring the operations to calculations that are easier to perform. Still using the example above: 67 x 89 = 67 x (90 - 1) = 67 x 90 - 67 = (60 + 7) x 90 - 67 = 60 x 90 + 7 x 90 - 60 - 7. The operation seems long but all the elements are simple calculations that you can perform quickly. Thus 67 x 89 = 5400 + 630 - 60 - 7 = 5963. Tying it back to the initial proposal, we turned multiplication into addition and substraction, which is much easier to do.
  • Know shortcuts and certain computations to speed up the calculation: To be exhaustive, below is a list of things that should be memorized beforehand:
    • Multiplication tables: They should be memorized and even extended to include multiplication tables up to 15 or 16 (or even 20 if you're brave enough);
    • Basic squares and cubes: Ideally all of them from 1 to 10 should be known to help you speed up some calculations;
    • Basic fractions: Mainly from 1 to 1/10. As weird as this sounds, fractions come in extremely handy when dealing with percentages: 25% can be replaced with 1/4 and 66% can be replaced with 2/3, instead of doing the calculations by hand;
    • Shortcuts: Multiplying numbers by 5 and ending with certain digits, multiplying numbers by 11, certain shortcuts relative to addition and substraction should be known. A quick Google search on math tricks should uncover most of these for you.
  • Use mental math apps and online tools to practice mental math: Nothing beats live practice and it's best to do it in an environment or with a tool that simulates the sense of urgency in a case interview. As such online mental math tools such as the one on PrepLounge and Victor Cheng's tool (http://www.caseinterview.com/mental-math) are good tools to practice with. There are many mental math apps available on the App Store and the Google Store but they are not really professional nor useful (Unless we're talking about those provided by Magoosh or other websites that offer training in numerical tests).
  • PRACTICE, PRACTICE, PRACTICE: need I say more? :)

Best of luck.

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Khaoula on Jan 17, 2017

Thanks for this useful tips :) Good luck with your interviews!

Sarah on Nov 11, 2017

That's a really nice overview! Thanks!

Originally answered question:

Any tips to do math calculations fast ?

Peter
Expert
replied on Jan 19, 2017
Ex-Bain & Company Case Team Leader * Placed 40+ MBB candidates as Partner in Europe's leading top-tier Consulting recruiting firm

Let me share a secret: There's no real benefit in the context of case studies in doing maths relatively fast. In fact, people worrying they're being too slow tend to make stupid mistakes by skipping steps.

"Being slow" at maths in cases generally means the person loses their way, or is trying to solve the wrong problem. Obviously it's a plus if you're a human Excel, but for most people the perfect case interview is simply clearly written down and talked through maths, starting with the problem in words, followed by numbers.

I always advise people to take their time, work through complicated numbers in detail on a separate sheet of paper if necessary and for 95% of people there will be no problem with speed.

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Anonymous replied on Jan 19, 2018

There are many sources u can use e.g.

1. Mental Maths Tool from Preplounge

2. Mental Maths Tool from Victor Cheng

3. GMAT Questions

4. IQ Test also include mental maths questions e.g. solving basic equations

But for basic mental maths the tool on PL and the tool of VC are sufficient. Besides of this u should also make sure that u know how to solve more complicated caluculations on a piece of paper. Good luck with ur prep.

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Originally answered question:

Any tips to do math calculations fast ?

Anonymous replied on Jan 16, 2017
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Vlad
Expert
Content Creator
replied on Jan 19, 2018
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School

Hi,

Basically, you need to develop 3 calculation skills:

1) Learn how to multiply double digit numbers (google fast math tips or The Veda math).

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) Use math tools (Mimir math for iOS, Math tool on Viktor Cheng website) to practice. Train, train, and train again

PS, Additionally I suggest to learn how to make the division mentally:

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

Good luck!

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John on Jan 19, 2018

Where can one find a division table with the decimals ? The classic one is only the obvious numbers.

Vlad on Jan 20, 2018

You can make it yourself with a calculator;)

Francesco
Expert
Content Creator
replied on Jan 20, 2018
#1 Coach for Sessions (3.900+) | 1.400+ 5-Star Reviews | Proven Success (➡ InterviewOffers.com | Ex BCG | 9Y+ Coaching

Hi Tiago,

I agree with Alexander, Vlad and Tania; I would also suggest you to:

  1. Write down the initial formula for the math computation. That’s not always feasible when you have to do mental math, but if possible try to always do so. I found many candidates start to do math without having clear what is the overall formula they have to use. This can lead to longer computations and therefore mistakes. Eg say you have to find the additional revenues from a new technology that increase revenues by 13% per employee. You have 180 employees. Current revenue per employee per month in this division is €1200. You want to find the annual increase in revenues.
    1. Option 1 (average): Compute current revenues per year (180*12*1200); then compute new revenues per year (180*12*1200*1,13). Then subtract.
    2. Option 2 (great): Write down the formula from the beginning. You can immediately spot you can aggregate the formula as (0,13*180*12*1200). You avoid a full computation that could lead to mistakes and appear faster in front of the interview at the same time
  2. Train math under pressure. Most of the mistakes done in math during the interview are not due to lack of math knowledge. Rather, to the fact that you have to do math under pressure and are not used to that. That’s actually what you should train for. Best thing would be to do math with a timer, setting it with a challenging constraint that will force you to train under pressure. Eg if you can do percentage exercises in 15 seconds each on average, train with a timer set at 12-13 secs. The fact and feeling you don’t have enough time will help you to train for pressure.

Best,

Francesco

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Alexander replied on Jan 23, 2020

With multiple-factor multiplications like these it is often a good idea to change the order of operations and group the numbers more efficiently.

As a first step, I would propose the following:

((25 * 8) * 1.4) * 220 * 23 = (200*1.4) * 220 * 23 = 280 * 220 * 23

As a second step, the 280 * 220 can be simplified using the distance-of-squares method. Both numbers are 30 away from 250, so you can calculate the result as follows:

280 * 220 = 250^2 - 30^2 = 62500 - 900 = 61600

Please note that there is a shortcut for squares ending in 5 that I've used here - basically, if you square a number ending in 5, take the non-unit digit, multiply it with itself + 10, and add 25.

And now the calculation boils down to 61600 * 23, which I would treat as such:

61600 * 23 = 61600 * 20 + 61600 * 3 = 1232000 + 184800 = 1416800

Hope this helps!

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Originally answered question:

Math training - how do you do it?

Anonymous A replied on Sep 27, 2016

Thanks for the replies guys!

I know (and use) caseinterviewmath.com as well. A good website indeed, but only for practicing. They don't provide "tips and tricks" on how to solve sums like the aforementioned. Of course, one way is to use paper, and this might indeed be enough for cases. But if someone does know some "tips and tricks" I would love to hear of them (also, some of these tricks might have to be performed on paper as well).

An example of the tricks I am referring to:

- 227 : 5 = ? Instead of computing it the long way (7*5+20*5+200*5) you can multiple the first number by 10 (to make 2270) and than take half of it (1135, which is the answer). Goes for any division by 5 obviously.

- 19*18 = ? Although this one is easy to do the conventional way, an alternative is the trick of (1) adding the first digit of the lowest number to the highest number (= 8 +19 = 27), then (2) multiply this by 10 (= 27 * 10 = 270) and then (3) adding the product of the first two digits of both numbers (= 9 * 8 = 72), resulting in 270 + 72 = 342. This only works up to a multiplication of the numbers UNDER 20.

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Czuee on Mar 05, 2017

I would do this in another way: First calculate 18*20= 360 which is easy, and then subtract 18 from it 360-18 = 342

Clara
Expert
Content Creator
replied on Jan 23, 2020
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

I would:

  • 1st: write the whole equation, just as you did in the post
  • 2nd: try to re-arrange it in a way in which you find easy relationships among numers (when possible) -e.g., 8*25 is 200, which multiplied per 220 is raughly 200 squared, etc.) This for sure depends on if you are allowed to round up numbers or not, which is something you should clarify with the interviewer)

Hope it helps!

Cheers,

Clara

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Guillaume replied on Jan 20, 2018

The only book you need is "Secrets of Mental Math" by Arthur Benjamin and Michael Shermer, for few bucks on Amazon.

Easy to "read", training pages, super useful tricks for cases and for your whole life : I don't understand why calculation is not tought like that at school...

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Tania replied on Jan 19, 2018
Experienced consultant looking for case partners to practice with - tjorge@live.com.au
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Gaurav
Expert
Content Creator
replied on Nov 10, 2020
Ex-Mckinsey|Certified Career Coach |Placed 500+ candidates at MBB & other consultancies

For practicing and improving your mental math you can find also some apps and tools, besides Victor Cheng’s math tool (Magoosh's mental maths app, Mental math cards challenge app etc). But there are some facts that will help in overall improvements:

Consulting math is very different from academic math. Working consultants - and consulting interview candidates - are always under time pressure. Results are what matter and answers are required simply to be good enough to guide business decisions, rather than being absolutely correct. The next important thing is that rather make it on the paper to structure the notes and then to communicate the results clearly rather than make your calculations fast

The time pressure in case interviews is severe and you cannot afford to waste time. But to make your calculations right you shouldn’t be in a rush. So, I would recommend you here to work on both - practice with time limitations and learn how to keep your mind peaceful and concentrated (it might be not so popular advice here, but mediations really make their job here ). Be comfortable and confident to state your answers not as a questions. Interviewers notice this, and this will not give a credit. If you need any further help or career advice, feel free to reach me out.

And here is math app for practicing math fractions and percentages from one of PL participant https://apps.apple.com/us/app/case-math/id1507653375?mt=8&ign-mpt=uo%3D4

Also, there is a tool provided by PrepLounge (https://www.preplounge.com/en/mental-math.php

Does it make sense to you?

GB

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Originally answered question:

Mental Math Skills

Anonymous replied on Jul 22, 2020
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Sash
Premium
Skilled
replied on Jan 23, 2020

I agree with Alexander. It is always easy to change the order and calculate. Preference should be given to those that result in round numbers. I would proceed in the following way:

First multiply 8*25 and then multiply the result 200 with 1,4. Till that it's quite simple. Multiplying 280 with 220 and 23 is the hard part. You can break 220 and 23 into 200+20 and 23. If you notice multiplying by 2 is not that difficult. So multiplying (200+20) with (23) would yield 4600+460 = 5060. Now multiply 280 by (10000/2 + 60) = 1,400,000+16,800 = 1,416,800

(25*8)*(1.4)*(200+20)(23) = 200*1.4*(4600+460) = 280*(5000+60) = 280*(10,000/2 + 60) = 1,400,000 + 16,800 = 1,416,800. If you find multipluying with 60 is hard, then you can break it into (100/2 + 10).

Hope this helps!

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Originally answered question:

Enhancing skills for mental math

Marco-Alexander
Expert
Content Creator
updated an answer on Sep 05, 2021
Former BCG | Case author for efellows book | Experience in 6 consultancies (Stern Stewart, Capgemini, KPMG, VW Con., Hor

(edited)

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Originally answered question:

Mental Math Skills

Egor
Expert
replied on Oct 04, 2018
Collected McKinsey & BCG offers/ Ex-McKinsey consultant/Harvard/WBS/MSU

Hi A,

Download mental math for your Iphone and practice everyday at least 10 min.

All the best,
Egor

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Originally answered question:

Math training - how do you do it?

Dorjan replied on Oct 14, 2016

google Vedic Math

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Originally answered question:

Any tips to do math calculations fast ?

Alec replied on Oct 08, 2018

There are a couple of good apps on the Apple App Store that you can use for practice.

Search "Case Math" and you'll find a few.

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Originally answered question:

Mental Math Skills

Guennael
Expert
replied on Oct 05, 2018
Ex-MBB, Experienced Hire; I will teach you not only the how, but also the why of case interviews

Caseinterviewmath.com will rank you by accuracy and speed, letting you know exactly where you stand against many thousands of MBB candidates

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Originally answered question:

Any tips to do math calculations fast ?

Anonymous replied on Sep 10, 2018

Hi Khaoula,

I'm a former McKinsey consultant, and I have a number of methods and recommendtions for doing caculations more efficiently, which leads to much faster calcuations and fewer mistakes.

I disagree with some other responses which say that doing math quickly isn't a benefit in an interview. I have had numeous peoeple who said htey used my methods to solve the quant problmes in Case Interviews quickly, and that the interviewer was defintely impressed. While it's true, that if you try to rush the math, you might make a mistake, you can learn specific methods that are simpler, faster and less error prone.

For example, what is 120 Million times 250? This could come up if they tell you a company sells 120 Million units per year, at $250 per unit. A typical approach would be to use Long-hand multiplication, or to caculate 12 × 25 and count zeroes. These both tend to be somewhat slow, and error prone, especially with counting zeroes.

Here's an efficient methods:

  • Decompose 250 into ¼ × 1,000
  • ¼ × 120 Million = 30 Million
  • 30 Million × 1,000 = 30 Billion (Million × Thousand = Billion)

There are a number of other methods like this, and I wrote some articles in the Bootcamp section on quant skills required in Case Interviews.

I have also created the FastMath Ace the Case online course specifically to teach the quant skills needed to succeed in Case Interviews — you can access the course here: http://www.fastmath.net/ace-the-case/?pc=preplounge_bc_001

Enjoy,
Matthew

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Originally answered question:

Math training - how do you do it?

Christina replied on Sep 30, 2016
I'm a physics graduate aspiring to be an APD associate. I'm looking for someone available to practice on weekends. Thanks!

There are books that teach those kinds of tricks. It's been a while since I've read one, but Rapid Math Tricks is an example book. You might find it at a library.

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Originally answered question:

Math training - how do you do it?

Anonymous C replied on Sep 28, 2016

Are there math drills with equations on some website, or like how it is given in a case usually? Story to math.

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Originally answered question:

Math training - how do you do it?

Andrew replied on Sep 27, 2016

I think for problems like this it is entirely appropriate to just work it out on paper. You could try to whiz through it with mental math calculations but I simply work the calculations on paper.

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