Division techniques

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New answer on Jul 08, 2020
6 Answers
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Chris asked on Feb 19, 2018
Prepping McK, Bain & BCG (2nd round)

Hi, I have final round at all 3 MBBs coming up in the next two weeks and would like to make sure I'm as prepared as I can be.

I'm fairly confident in my quant skills, but my only real insecurity remaining is divisions. I'm just not good at it: I don't know a lot of shortcuts and for those divisions where no shortcuts apply, I have a really hard time doing the math.

For instance: 6,300,000 divided by 7,200. I just have absolutely no idea how to tackle this. My best try is to attempt long division, meaning the long and painful process of telling myself:

(1) Basically figure out how much is 630/72 and then add the zero's.

(2) Ok 72 doesn't fit 10 times in 630, how about 9? No neither, ok it fits 8 times.

(3) Ok how much is 72*8? It's 576, so 630-576 = 54.

(4) Ok let me make this 540 and see how much 72 fits into this, and I'll divide by 10 later.

(5) etc ...

Any advice at all please? How would you calculate 6,300,000 divided by 7,200, or any other large division of the kind?

A sincere thank you in advance!

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Vlad
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replied on Feb 19, 2018
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School

Hi,

There are two techniques that you can use:

1) 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 lose zeros and all multiplications/divisions will be replaced with + or -.

In your case, it will look like 63 * 10ˆ5 / 72 * 10ˆ2

2) If you need the precise calculation - you can use the basic division technique, calculating 630 / 72 * 10ˆ2 = 875

3) If you don't need it precise - Learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems

In your case, it will be roughly 6/7 * 10ˆ3 = 85.7 * 10ˆ3 or 857. Since I know that it was the rough calculation and the real number should be bigger, I would round the final result to 870

Best!

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Chris on Feb 20, 2018
Hi Vlad, thanks for responding. 1) I already use, 3) I forgot about but is very useful indeed. On 2), could you elaborate how you do the basic division technique? Do you use long division and write it out?
Juan Pablo replied on Feb 19, 2018
I did my internship in consulting and now I am preparing actively for interviews

You could realize that in order to have the same number of zeros, you would need 000 ( three zeros) so you would have to multiply it for 1.000. After that, you would have 7.200.000, however thats bigger that the number of you need, so try to think about what percentage of the number you woud need.

In this situation you could figure out that you would need about 15% less than your actual number, so you rest 15% of 1.000 and that would be around 850, which is not that far from the answer of 875.

Have in mind that depending on the situation, you would need to do the math calculation exactly and you could not round up the numbers. In this case, just do the traditional division process

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Francesco
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replied on May 31, 2018
#1 Expert for Coaching Sessions (3.600+) | 1.300+ Reviews with 100% Recommendation Rate | Ex BCG | 8+ Years of Coaching

Hi Chris,

in the specific example you provided, I would consider the following:

  1. Cut unnecessary 00. This reduce the equation to 63.000 / 72
  2. Transform the equation in 63/7.2 * 10^2
  3. Perform the division of 63 / 7. This will give you 9. Your solution will be thus close to 900
  4. As you know the actual divisor is 7.2, you know the first number is 8
  5. 7.2*8 =57.6. Thus 5.4 as a difference
  6. Repeat previous process. 54/7=7. As this is the second number, solution should be close to 870
  7. Continue the process according to the simplification you need

Best,
Francesco

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Anonymous updated the answer on Jul 08, 2020

Dear Chris,

Remember here about estimating and adjusting.

For example: 96,840/529

Step 1: Estimating

We will have a simplified version of: 96.84/52.9, taking out 3 zeros in the numerator and 1 zero in the denominator which means that we will return 2 zeros in the last step.

Technically we need a step of “rounding” here. But in this case, we can just skip it and make an overall adjustment later.

Now turn division into multiplication and find x:

52.9 x ? = ~96.8

We know 53 x 2 = 106

Thus, ? is a little bit lower than 2.

Step 2: Adjusting

With a downward adjustment for 2, we have 1.8. And with zeros, it is 180.

The correct answer is 183.06

Hope it helps,

Best,

André

(edited)

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Andrea
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Content Creator
replied on Feb 25, 2018
Former BCG Principal and decision round interviewer

If you feel uncomfortable with divisions, I would just stick with long division technique and keep your neves steady. I second the suggestion of using powers of 10. I would advise against memorizing division tables because under pressure you might misremember, forget and get flustered. Also using methodology suggested under (3) might elica different reactions from interviewer: some might appreciate it, others might not and get ticked off by it (too many roundings and then an arbitrary reverse rounding to correct for it) or, even worse, think you aren’t able to do divisions at all.

If you still would like to use (3) because you feel super-comfortable in remembering the key divisions, but want to avoid potential repercussion would ask for permission before proceeding with it.

Andrea

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Vlad gave the best answer

Vlad

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