Hi,

I am not completely sure **whether you are talking about the general calculations or a market sizing quant problem.**

If it is the **general math**, you follow these steps:

- Take a minute to think about the problem
- Provide the formula / your approach to calculations / equation
- Check with the interviewer whether it's correct
- Continue calculations, coming back to the interviewer with some intermediate numbers
- Come up with a final number and check it with the interviewer.

If it is a **market sizing problem**, there are several things you should know:

1) First of all, there are **two ways to calculate market size:**

- From supply side (e.g. vending machines spots)
- From demand side (e.g. vending products consumption)

2) There are **2 ways to structure market sizing:**

- Formula - basically a math formula to come up with a solution. The problem with the formula is that it is easy to forget something or get lost.
- Tree - same as with regular cases you build a tree. A very simple example: you need to calculate the number of dogs on manhattan. A number of dogs = share of households having a dog * # of households. # of households = population / average household size. In the end, you'll have a pyramid where you have to fill the numbers on the base of the pyramid. This approach is much easier and help you track all the numbers

3) You should **use the key market sizing techniques:**

- Making assumptions based on personal experiences (Use the example of your house where out of 100 apt-s 10 have dogs)
- Adjusting numbers (NY is a busy city thus fewer people have dogs)
- Sanity check - try to apply your calculations to real environment
- etc.

4) You should **learn and use the key tools:**

- Using age even age split (suppose life expectancy is 80 years. Assuming even age split we have 4 mln people in US of each age group)
- Using 80/20 split (suppose 20% people earn 80% wealth and the average salary is xx...)
- Using approximations (Length of NY-SF flight and plane speed to calculate US length)
- etc.

5) **Learn and use the key numbers**: populations, gas price, gas consumption, Boeing speed and nmber of seats, average salary, # of gates in the airport, GDP growth rate, inflation, etc.

Good Luck!