I would answer this question on the basis of my preparation experience and would include relevant examples to juice it all up. Firstly, let us list down what stuff might be relevant for the interviewer to give you a good evaluation, in decreasing order of priority.
1. A Structured approach
2. What general numbers should I remember?
3. Math: Numbers galore
4. Handy Formulae
1. A Structured approach
So, the torture has started. You have been asked a question which doesn’t seem to have any relevance in ANY Universe. What do you think should ensue? Chaos, Panic ! Tears roll down your eyes, piss down your pants. Well, this is exactly what must be avoided. So, some ways to add method to the madness, are as follows:
Clarify, Clarify ….. Clarify !!!! “ The first step to solving a problem is to know it.” So it is essential to have a COMPLETE picture of what you need to estimate
Contraceptive Example: (Yeah!! No need to feel shameful. Interviewers do ask such questions.)
Curious Interviewer: “What is the number of people using contraception in a night?”
Much more Curious Interviewee: “I have the following clarifying questions” (asks them one by one).
“Which month is this night in?” This matters, since; marriages in India are concentrated in December, due to religious reasons, ultimately leading to an increased number of contraceptive users.
“Is the required number to be calculated for the World or India?” The interviewer might have purposefully left out the fact that the question was India specific.
“What are the different contraceptives?” No matter how sincerely you had taken your sex education class in school, you might want to clarify this point too.
Try having ‘n’ methods to estimate: So, let’s say, you have started using a particular approach and midway into the discussion you realise that a different approach will give a much better estimate. What do you do? You are faced with the and hence continue with your inefficient approach.
So, the solution to this is fairly obvious. Have a list of ‘n’ approaches upfront and subsequently choose one which seems most apt.
Contraceptive Example: You could estimate this from the Demand side (number of people who WISH to have protected sex) or from the Supply Side (number of people who CAN have protected sex). Now, in rural populations, the Supply<Demand, and in urban populations, Supply=Demand. So, the calculations for urban populations can be done from both the Supply and the Demand side. However, for rural populations the Supply side will give the right estimate.
Go Old School: Write a formula ! : You want to find a number which is basically a combination of other numbers. So, write the relationship between your required number and the other numbers (basically, write a formula). Now, all that is left is finding the numbers on the RHS independently and Presto! You have your guesstimate.
Contraceptive Example: Going from the Demand Side. “Number of contraceptives used = Number of couples having sex per night*Fraction having protected sex* Number of contraceptives used per couple per night”
Backward Traceability: The idea is to write the calculations; the tree diagrams etc. in a chronological manner such that if at any point in time, you want to go back and check your calculations or approach you can do it without any fuss.
2. Awareness in General: What general numbers should I remember?
The following numbers can be memorized for your country (here India)
*Only ballpark figures are mentioned
GDP = 1.8 trillion USD
Population = 1.2 billion ~ 1 billion
Land Area = 3 million km^2
GDP growth rate = 5%
Average size of a family = 3.6 ~ 4
Number of households = 330 million ~ 300 million
Population growth rate = 1.5 % ( World = 1%)
Sex ratio = 1:1
Rural: Urban population = 70:30
Population Distribution by Age:
India has a young population. It has more than 50% of its population below the age of 25.
0-15: 30 %
15-25 : 20 %
25-50 : 30 %
50+ : 20%
Population Distribution by Income:
Upper Middle Class (>32,000 pm): 10%
Middle Class (16,000-32,000 pm): 30%
Lower Middle Class (8000-16,000 pm): 40%
Below poverty line (<8000pm): 20%
Mumbai population = 20 million
Kolkata, Delhi population ( Take Approx same for all metros ) =15 million
3. Math: Numbers galore
Number of Zeros : 1 lakh = 10^5, 1 million = 10^6, 1 crore = 10^7, 1 billion = 10^9, 1 trillion = 10^12
Percentages: Situations arise when you have to multiply percentages. So it is good to have this well practised. Example: In a population 80% males and 60% females wear watches. Then, assuming a 1:1 sex ratio we get 80%*50% + 60%*50% = 40% + 30% = 70% of the population wears watches.
4. Handy Formulae
Market Size: Estimating the market size would basically mean, how many new products will be required in the next year.
# Products required per year= # existing products that get obsolete + # new products required
= Q/n + r*Q
Where, Q= existing number of products in the market
n= average age of the product
r= average growth rate of the product~ GDP growth rate of the country ( 5% for India )
Example: “What is the market size of squash rackets in India?” The average age of a racket (n=1.5 yrs), average growth rate for the racket (r= 5%) and the number of existing rackets in India (Q = 1 million has to be found by guesstimation). Market size = 1 million * ( 1/1.5 + 0.05 ) = 0.72 million
Occupancy: This is valid for any situation in which there are a particular number of places and a partial number of them are occupied. Thus, like a bus, theatre, stadium etc. have ‘n’ seats and a fraction of them are occupied.
Example : Avg occupancy of a particular bus is 70%, then if there are 100 seats, at any point in time on an average 70 seats will be occupied.
Example : “Q: What is the market of roses in India?”. Here, you must think that roses are not just sold as a flower but also is a raw material for the production of rose water. Hence, it is important to include this hidden application in your guesstimate.
Example: During the course of investigating any costs for a guesstimate of total costs, you might encounter a situation like, what is the cost of potatoes per Kg and you have no freaking idea. Solution: Estimate the weight of a samosa (30g) and the cost of the cheapest one that you have eaten (say, Rs 5) and assume a % of this samosa’s cost which would come from the potato ( say, 20% : This number is low because oil is an essential component in samsosa making which is definitely expensive) . Thus, the cost of potatoes in Rs per Kg then is = (5*20%)/(0.030) ~ 35.
I will keep on adding anything else that might seem relevant over the course of time.