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Sidi

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9

Fast Maths Expectations | MBB

Hi PrepLounge community,

I have seen crazy records in the 'Mental Maths' section of PrepLounge and I would really appreciate some clarification.

What is the expectations for fast maths in MBB? This is my current situation after some training:

  • I can perform quite well mentally all the basic calculations: - Additions and subtractions up to three digits (e.g. 365 - 174) - Basic multiplication that include 25/75/50/100 - Basic fractions - 'Ballpark' calculations --> In maximum 10 seconds and with a low percentage of mistakes (hopefully!)
  • Yet, I need to write down (as I did in elementary schools) the toughest calculations - Additions and subtractions of 5+ items, or 4+ digits - Toughest fractions - Divisions by two-plus digits - Multiplications by two-plus digits without easy shortcuts --> I can do this in maximum 30 seconds, but it's still writing down while the interviewer knows the final number.

1) Is this normal?
2) And how can I better 'manage' the toughest calculations from a communication perspective: I don't want to lose track of the interviewer, but I need to regroup and focus on the on-paper calculations?

Thank you so much!

Anonymous

Hi PrepLounge community,

I have seen crazy records in the 'Mental Maths' section of PrepLounge and I would really appreciate some clarification.

What is the expectations for fast maths in MBB? This is my current situation after some training:

  • I can perform quite well mentally all the basic calculations: - Additions and subtractions up to three digits (e.g. 365 - 174) - Basic multiplication that include 25/75/50/100 - Basic fractions - 'Ballpark' calculations --> In maximum 10 seconds and with a low percentage of mistakes (hopefully!)
  • Yet, I need to write down (as I did in elementary schools) the toughest calculations - Additions and subtractions of 5+ items, or 4+ digits - Toughest fractions - Divisions by two-plus digits - Multiplications by two-plus digits without easy shortcuts --> I can do this in maximum 30 seconds, but it's still writing down while the interviewer knows the final number.

1) Is this normal?
2) And how can I better 'manage' the toughest calculations from a communication perspective: I don't want to lose track of the interviewer, but I need to regroup and focus on the on-paper calculations?

Thank you so much!

Anonymous

9 answers

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Book a coaching with Sidi

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Hi Anonymous!

I have written this earlier, and I will repeat it: the obsession with "Mental Math" is one of the many damaging nonsense myths that are flying around! Mental math is simply not something that is required in ANY way!

  • In MBB, you are NOT tested for doing math stunts in your head, but for the rigor and correctness of your analysis.
  • You will NOT get bonus points for being lightning fast!
  • You WILL get bonus points for being very clear and easy to follow.

This means, the skill you have to build is to quickly identify what you need to analyze and why, and organizing this in a way that you can work through this in a very linear and easy to follow manner. Hence, I recommend to ALWAYS use pen and paper for your analysis (e.g., using tables works very well in many situations).

At the extreme, being exceptionally fast in mental math will even HURT your case performance! The reason is simple: the interviewer will always assume that the way you behave in an interview is also how you behave vis-a-vis a client. If you become a human calculator, doing all sorts of complicated math stunts lightning-fast in your head, then you become VERY HARD TO FOLLOW. Hence, the quality of your communication deteriorates. And this is always your fault, not the client's!

So in essence, make sure that you are doing clear and very easy-to-follow calculations, using pen and paper to write down the required steps first and then to perform the actual computation. Trying to become a lightning fast human calculator has a lot of risks and practically no benefit.

Cheers, Sidi

Hi Anonymous!

I have written this earlier, and I will repeat it: the obsession with "Mental Math" is one of the many damaging nonsense myths that are flying around! Mental math is simply not something that is required in ANY way!

  • In MBB, you are NOT tested for doing math stunts in your head, but for the rigor and correctness of your analysis.
  • You will NOT get bonus points for being lightning fast!
  • You WILL get bonus points for being very clear and easy to follow.

This means, the skill you have to build is to quickly identify what you need to analyze and why, and organizing this in a way that you can work through this in a very linear and easy to follow manner. Hence, I recommend to ALWAYS use pen and paper for your analysis (e.g., using tables works very well in many situations).

At the extreme, being exceptionally fast in mental math will even HURT your case performance! The reason is simple: the interviewer will always assume that the way you behave in an interview is also how you behave vis-a-vis a client. If you become a human calculator, doing all sorts of complicated math stunts lightning-fast in your head, then you become VERY HARD TO FOLLOW. Hence, the quality of your communication deteriorates. And this is always your fault, not the client's!

So in essence, make sure that you are doing clear and very easy-to-follow calculations, using pen and paper to write down the required steps first and then to perform the actual computation. Trying to become a lightning fast human calculator has a lot of risks and practically no benefit.

Cheers, Sidi

(edited)

honestly this is such a relief to hear and thank you sincerely for such a thorough and informative reply — Anonymous B on Apr 21, 2020

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Hello,

The fact that you have to show outstanding math skills during case interviews is only a myth. The only real requirement is not to do any mistake, giving always the right result at the first answer.
Mental calculation is a nice plus, but it's perfectly fine to use a pen and a paper to do your calculation. I suggest to use a different sheet to do your calculation and to report only the result on the original sheet.

Best,
Luca

Hello,

The fact that you have to show outstanding math skills during case interviews is only a myth. The only real requirement is not to do any mistake, giving always the right result at the first answer.
Mental calculation is a nice plus, but it's perfectly fine to use a pen and a paper to do your calculation. I suggest to use a different sheet to do your calculation and to report only the result on the original sheet.

Best,
Luca

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Totally agree with Sidi. Speed is not the top nor the deciding factor. You need to do the math right in a client friendly way - clearly articulate how you do it and make sure your client follows you. When every other factor (approach/logic/articulation) is equal, of course fast is better than slow. But if you mess up one of those factors or lose your audience, fast would do you no good.

Emily

Totally agree with Sidi. Speed is not the top nor the deciding factor. You need to do the math right in a client friendly way - clearly articulate how you do it and make sure your client follows you. When every other factor (approach/logic/articulation) is equal, of course fast is better than slow. But if you mess up one of those factors or lose your audience, fast would do you no good.

Emily

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Hi there,

I agree with Sidi that trying to do everything in your head can bring more problems than benefits. It is far better to clearly communicate your approach and avoid mistakes rather than being superfast. Having said that, of course you also don’t want to be incredibly slow.

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. As mentioned, it is totally fine to write it down.
  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.

Best,
Francesco

Hi there,

I agree with Sidi that trying to do everything in your head can bring more problems than benefits. It is far better to clearly communicate your approach and avoid mistakes rather than being superfast. Having said that, of course you also don’t want to be incredibly slow.

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. As mentioned, it is totally fine to write it down.
  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.

Best,
Francesco

(edited)

Book a coaching with Thomas

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Totally agree with what the others have said. You won't get an offer because you are a little faster than others. Having said that, I do advise to practice some simple mental math just so that it is fresh and you are not caught off guard.

Totally agree with what the others have said. You won't get an offer because you are a little faster than others. Having said that, I do advise to practice some simple mental math just so that it is fresh and you are not caught off guard.

Book a coaching with Udayan

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Mental math is an important case interview skill, but as pointed out by Sidi it is not the core skill that is being tested in interviews. The main thing here is to ensure you can do the calculations reasonably fast and always accurately. There are no points awarded for doing it in lightning fast speed.

In terms of difficult calculations - the most important part of the analysis section is the setup. Once you communicate the approach to the interviewer the math portion itself is rarely that challenging.

Best,

Udayan

Mental math is an important case interview skill, but as pointed out by Sidi it is not the core skill that is being tested in interviews. The main thing here is to ensure you can do the calculations reasonably fast and always accurately. There are no points awarded for doing it in lightning fast speed.

In terms of difficult calculations - the most important part of the analysis section is the setup. Once you communicate the approach to the interviewer the math portion itself is rarely that challenging.

Best,

Udayan

(edited)

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If it consolates you, I also had to write down the "long" and complex ones in a school-way and it didn´t harm me!

If it consolates you, I also had to write down the "long" and complex ones in a school-way and it didn´t harm me!

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Hi,

I would be happy to share few insights on how to better tackle quick maths BUT you should take into account that it should be your last priority in preparation. MBB focuses on accurate calculations and interpretation of graphs vs speed of calculations.

So let's get on to the practice:

  • The "9-trick"

To add 9 to any number, first add 10, and then subtract 1. For example, we change the addition 9 + 4 to 10 + 3, which is much easier to solve. But this "trick" expands. Can you think of an easy way to add 73 + 99? Change it to 72 + 100. How about 485 + 999? How would you add 39 + 27 in your head? Let 39 become 40… which reduces 27 to 26. The addition is now 40 + 26.

  • Doubles + 1

Memorize the doubles from 1 + 1 through 9 + 9. After that, a whole lot of other addition facts are at their fingertips: the ones we can term "doubles plus one more". For example, 5 + 6 is just one more than 5 + 5, or 9 + 8 is just one more than 8 + 8.

  • Use addition facts when adding bigger numbers

Once you know that 7 + 8 = 15, then you will also be able to do all these additions in your head:

70 + 80 is 15 tens, or 150

700 + 800 is 15 hundreds, or 1500

  • Subtract by adding

​This is a very important principle, based on the connection between addition and subtraction. You really don't need to memorize subtraction facts as such, if you can use this principle. For example, to find 9 − 6, think, "6 plus what number makes 9?" In other words, think of the missing number addition 6 + ___ = 9. The answer to that is also the answer to 8 − 6.

This principle comes in especially handy with subtractions such as 13 − 7, 17 − 8, 16 − 9, and other basic subtraction facts where the minuend is between 10 and 20. But you can also use it in multitudes of other situations. For example, 63 − 52 is easier to solve by thinking of addition: 52 + 11 makes 63, so the answer to 63 − 52 is 11.

  • Five times a number

To find 5 times any number, first multiply that number times ten, then take half of that. For example, 5 × 48 can be found by multiplying 10 × 48 = 480, and taking half of the result, which gives us 240.

  • Four and eight times a number

If you can double numbers, you already have this down pat! To find four times a number, double that number twice. For example, what is 4 × 59? First find double 59, which is 118. Then double that, and you get 236.

Similarly, eight times a number just means doubling three times. As an example, to find 8 × 35 means doubling 35 to get 70, doubling 70 to get 140, and (once more) doubling 140 to get 280. However, personally I would transform 8 × 35 into 4 × 70 (you double one factor and halve the other), which is easy to solve to be 280.

  • Multiply in parts

This strategy is very simple, and in fact it is the foundation for the standard multiplication algorithm. You can find 3 × 74 mentally by multiplying 3 × 70 and 3 × 4, and adding the results. We get 210 + 12 = 222. Another example: 6 × 218 is 6 × 200 and 6 × 10 and 6 × 8, which is 1200 + 60 + 48 = 1308.

Hope this helps,

Anton

Hi,

I would be happy to share few insights on how to better tackle quick maths BUT you should take into account that it should be your last priority in preparation. MBB focuses on accurate calculations and interpretation of graphs vs speed of calculations.

So let's get on to the practice:

  • The "9-trick"

To add 9 to any number, first add 10, and then subtract 1. For example, we change the addition 9 + 4 to 10 + 3, which is much easier to solve. But this "trick" expands. Can you think of an easy way to add 73 + 99? Change it to 72 + 100. How about 485 + 999? How would you add 39 + 27 in your head? Let 39 become 40… which reduces 27 to 26. The addition is now 40 + 26.

  • Doubles + 1

Memorize the doubles from 1 + 1 through 9 + 9. After that, a whole lot of other addition facts are at their fingertips: the ones we can term "doubles plus one more". For example, 5 + 6 is just one more than 5 + 5, or 9 + 8 is just one more than 8 + 8.

  • Use addition facts when adding bigger numbers

Once you know that 7 + 8 = 15, then you will also be able to do all these additions in your head:

70 + 80 is 15 tens, or 150

700 + 800 is 15 hundreds, or 1500

  • Subtract by adding

​This is a very important principle, based on the connection between addition and subtraction. You really don't need to memorize subtraction facts as such, if you can use this principle. For example, to find 9 − 6, think, "6 plus what number makes 9?" In other words, think of the missing number addition 6 + ___ = 9. The answer to that is also the answer to 8 − 6.

This principle comes in especially handy with subtractions such as 13 − 7, 17 − 8, 16 − 9, and other basic subtraction facts where the minuend is between 10 and 20. But you can also use it in multitudes of other situations. For example, 63 − 52 is easier to solve by thinking of addition: 52 + 11 makes 63, so the answer to 63 − 52 is 11.

  • Five times a number

To find 5 times any number, first multiply that number times ten, then take half of that. For example, 5 × 48 can be found by multiplying 10 × 48 = 480, and taking half of the result, which gives us 240.

  • Four and eight times a number

If you can double numbers, you already have this down pat! To find four times a number, double that number twice. For example, what is 4 × 59? First find double 59, which is 118. Then double that, and you get 236.

Similarly, eight times a number just means doubling three times. As an example, to find 8 × 35 means doubling 35 to get 70, doubling 70 to get 140, and (once more) doubling 140 to get 280. However, personally I would transform 8 × 35 into 4 × 70 (you double one factor and halve the other), which is easy to solve to be 280.

  • Multiply in parts

This strategy is very simple, and in fact it is the foundation for the standard multiplication algorithm. You can find 3 × 74 mentally by multiplying 3 × 70 and 3 × 4, and adding the results. We get 210 + 12 = 222. Another example: 6 × 218 is 6 × 200 and 6 × 10 and 6 × 8, which is 1200 + 60 + 48 = 1308.

Hope this helps,

Anton

Book a coaching with Antonello

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In interviews the aspect which causes more errors is pressure: start to solve calculations with strict time constraint. For longer formulas always share the calculation structure with interviewer before starting to write down the numbers: this helps to take time, to reduce the pressure and gives you the opportunity to receive a first feedback by the interviewer avoiding wrong calculations.

I recommend practicing with:

Best

Antonello

In interviews the aspect which causes more errors is pressure: start to solve calculations with strict time constraint. For longer formulas always share the calculation structure with interviewer before starting to write down the numbers: this helps to take time, to reduce the pressure and gives you the opportunity to receive a first feedback by the interviewer avoiding wrong calculations.

I recommend practicing with:

Best

Antonello

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