Keep it Simple
The below case resulted in the feedback of that I am really analytical and smarter than most people in their office but too detailed approach not being able to creatively quickly change thinking on the spot, also they mentioned if something like this happens you need to interaction with the interviewer to come to a solution together which i didn't do..
to give you the detailed question which dinged me:
what is the total economic costs for the country caused by traffic jams in the morning and evening?
I think i was stupid and started wrongly..
I said we need to know :
1) the amount of people in traffic jam 2) the time they spend in traffic jam 3) times the opportunity costs per hour
for 1) i first calculated by population based estimate the amount of people who are working in the country (calculation based upon each age country how many people are working etc) , then I assumed they all have a car but all only 50% uses them so you get the total number of people in traffic jam
then i thought they drive about 15 km / hour in a traffic jam, we know there is 400 km of traffic jam during 2 hours in the morning, 2 hours of traffic jam of 300 km in total in the evening then I got stuck..... and couldn't turn the case around anymore...because i was stuck with the concept that during 2hours there are continously 300 km and 400 km total 700 km of traffic jam, i tried to calculate how many people in the traffic jam on average etc etc but couldnt see it anymore
when i thought after it afterwards i felt its much easier just assume people in this country spend on average 0.5 hour per day in traffic jam (which is actually true), then calculatue amount of cars based on households( 6 m household all have 1.5 car) so 9 m cars of which apro.x 50% uses the car for work so we get
0.5 * 50% * 9 m * 250 days * 20( average gross salary per month is 3200 divided by 40-hour workweek) and divided by 4 weeks)= total opportunity costs of traffic jams=1125million=1.125 bn
one needs to practise , practise and practise , if you fail one case you are dinged automatically
Your second approach was the approach I would have used personally if I were the interviewee and the one I would have expected as an interviewer. The feedback on your first approach was that it was too detailed. I would probably have phrased it differently. Your first approach was... unnecessarily complicated.
You crunched more complicated numbers even though you didn't have to. The numbers were so complicated that you got confused and stuck in the middle of your own solution. If that's the case, you can be sure that a client would also get stuck trying to follow your explanation.
Incidentally this kind of estimation question is used on the job CONSTANTLY... usually prompted by client completely unexpectedly (so you can't tell a client it's unfair question). You have to be able to ballpark the answer in front of the client AND do it in a way that he or she can follow the math.
I once interviewed a graduated of ITT - The Indian Institute of Technology. He graduated with a PhD in Electrical Engineering (I think or it might have been Physics) AND he was #1 in his class. As I understand, this is a ridiculously impressive accomplishment -- clearly way more brain power than me.
I don't remember what case I gave him, but I remember his answer and my reaction.
My question was probably something like if a client that's an auto manufacturer asked you to figure out what kind of car to build for next year, what would you do? (Or something along those lines)
His answered involved putting tracking devices on 100,000 cars and using some super technical statistical analysis that I had never heard of (and I am familiar with a number of them) to create some super sophisticated projection model of what their behaviors suggested about what they wanted.
(This wasn't his exact answer, and I embellished it a little to make a point)
I'm sure his approach was mathematically correct, but the main problem was his answer was impractical from a cost standpoint -- even though theoretically it would work.
The answer I was looking for was:
Ask the customer what they want
Again, this wasn't the exact case and I can't remember what I asked.... and I'd never give a case where the actual right answer is "ask the customer for what they want", but I use this example to illustrate my reaction to the candidates theoretically correct, but real-world impractical, response.
Always take the simplest approach possible to get the answer. You'll be less likely to make a mistake and it's more likey a client (and an interviewer) can follow it.
And yes, practice makes perfect on estimation questions. I did at least 30 practice estimation questions before doing a real one in front of an interviewer. I would just walk down the street, spot random objects, and start estimating market sizes or whatever metric seemed interesting about this object.
I would do this walking to and from class - about a 5 - 7 minute walk - perfect for 1 estimation question.