# Consulting Math Consulting Mental Math

## Mental Math Is The key In Consulting Math

The nature of math in consulting contexts allows this methodology to excel.

1. You will encounter lots of them. So many that no one can survive without being decent in this.
2. The calculations need REALLY FAST RESPONSES. So fast that even the act of pulling out a calculator and inputting numbers is already “too long”.
3. Up to 5% margin for error is acceptable. This is true for all Case Interview, PST, and real consulting context. Speed is much more important than perfect accuracy.

The priority for SPEED dramatically changes the way we approach Mental Math. Let’s find out.

## Secrets Of Mental Math

In the estimation phase, we round the number into the simple version we can easily work with. In the adjustment phase, we take the result and adjust up or down for the rounding we did earlier. Let’s look at an example.

### No.1:

Example: 8710 x 594

Step 1: Estimating

We will have a nice simplified version of: 8.7 x 5.9, taking out 5 zeros in total.

9 x 6 equal 54

It’s important to adjust the rounding before putting in the zeros. Both of the above rounding need some downward adjustment, so I would ballpark it to be a rather big adjustment. 54 will be adjusted to 51.

So the final answer is 5,100,000.

Next step is to round:

8.7 now becomes 9, so it needs some downward adjustments later.

5.9 now becomes 6, so it also needs a tiny bit of downward adjustments later.

————————————————————————————————————————-

A more precise version?

From the 8.7 we have, examine 2 ends of possible rounding:

8 x 6 is 48

9 x 6 is 54

So 8.7 x 6 is somewhere between, but closer to 54 of course. Even more specifically, 8.7 is two third way from 8 to 9. So the final answer is somewhere 2 third way from 48 to 54 too. 52 seems to be a good estimation. And adjust a little bit down for the 5.9 instead of 6; 51.5 seems right!

Putting the zeros in, we have 5,150,000.

Did you get the idea?

### No.2:

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.

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

### No.3:

Example: 70% of 15,940

Step 1: Estimating

Multiply: 70 x 15,940

Take out 4 zeros and rounding, we have: 7 x 16

That equals 112.

Adjust it down a bit, we have 111.9, return 4 zeros, and take out 2 zeros original from the percentage sign, our answer is 11,190.

Applying this methodology in every calculation problems you encounter in life, you will get better really quick. The more your train, the better your brain can grasp this method and eventually be very fast yet precise in the adjustment phases.

You may also want to understand more about consulting math, gaining deeper insights of the most popular questions in both consulting interviews and written tests.

## Comprehensive Math Drills (All Math Questions & Cases)

This practice package contains the following:

• 30 chart problems
• 50 full-context cases
• 300 short math questions
• Over 1000 raw number calculations
• 10 Quantitative Cases

All complete with full keys and explanations 