When I was in my interview for my current company, the manager engineer asked me: "How many cows are there in Canada?"
So... how would all of you answer that?
I'd need more information around the context of the question to give a more effective answer.
Furthermore, smart arse trick questions like these which put the interviewee under unrealistic, unnecessary and undue pressure simply indicate to me they're not a particularly nice place to work in, and have too much time on their hands not doing real work. Can you imagine how intrusive and overbearing their HR dept is likely to be in your daily working life? No thanks!
Either you Just Get It(R), or you understand what one of these questions is getting at; or... you don't get it at all and you get frustrated with the whole idea.
What's the idea? Orders of magnitude. IGNORE REAL NUMBERS, COMPLETELY. Scary? Why? How is it any more scary than rounding a number to any other arbitrary precision? See, the idea generalizes, too! That is why it is useful.
1. There's about 10M people in Canada. (Why? Well, Canada is smaller than the US, and the US is about 100M, so it must be around 10M.)
2. A person eats about a pound per week of steak, and there are a hundred weeks in a year. (The first is an underestimate, and the second an overestimate. Justifying rounding like this is okay, just don't sit there thinking about how all the rounding stacks up, you'll take forever.)
3. A cow lives about 10 years before slaughter.
4. A cow is made of about 1000 pounds of steak.
Therefore, there's about 10B pounds of steak consumed in 10 years, and 10M cows to supply it (in equilibrium).
Or in short, about as many cows as people, which might be an easy shortcut. (On that note, pigs are about 1/10th the size of cows, so you'd expect 10 times more. Chickens live much less than a year, so should number about the same as pigs.)
Multiplying orders of magnitude is adding exponents, so you can do it in your head without jotting down a single thing on paper. Anyway, if this sort of question pops up out in the field, you won't have access to the internet anyway, and maybe not the pad of paper either!
Such arguments are great for ballparking whether something is even feasible at all.
The technique I think was first popularized as Fermi's estimation method. Of course, a man of that intellect would be more than comfortable processing the numerical value as well as the exponent, but the average joe can still get within a factor of 10 or 100 without any real practice!
Tim