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My guess is that they're looking for "your friend's" thought process while answering the question. Unless of course, there's more to the question you're letting on. One direction you could go is to assume that "man-made" and "woman-made" are distinct, so you'd take all the structures that were built, then subtract those that were built (however you choose to define "built") by women, then calculate the area of the resulting group and it's respective % of the US. Or, maybe, you could define "man-made" to include everything that wouldn't otherwise exist if not for humans, which could include mines, ski slopes, replanted forests, etc. Essentially defining "structure" however "your friend" chooses.
In short, it looks hard as shit because it's impossible without a lot more information, which is what leads me to think that they don't really care about the eventual answer; only the thought process.
42%
I'd say
Part of why i hate these questions is that if you wanted to test my thought process you could sit there and punch holes in my assumptions all day.
Me: So the US is about 3% lake and rivers. Interviewer: Where are you getting that? Me: Top of my head
Me: And mountain ranges are about 12% of the US. Interviewer: Source? Me: Ummm
I just dont see the point in watching someone spout off about stats that aren't backed up anywhere.
Your level of discomfort with the questions is indicative of your level of discomfort with having to approach an ambiguous problem in a structured way. Problems in the real world are not very similar to cases; they're actually closer--in terms of problem-solving--to the complex estimation questions. So you're completely right: they're not interested in the answer, only in the thought process.
I would approximate the U.S. as a rectangle 3,000 miles long by 1,000 miles high, for a total of 3,000,000 square miles. Converting to metric and rounding to make the later math easier, let's call it 10,000,000 square kilometers. I don't consider roads, fields, mines, etc. to be "structures," so I will not count them. I'll take a leaf from zoning ordinances and consider 3 types of structures: residential, commercial, and industrial.
Residential: I believe there are approximately 100,000,000 households in the U.S. and I'll estimate that each has a footprint of 100 square meters (smaller than the average house to accommodate high rises), for a total coverage of 10,000,000,000 square meters (10 square kilometers). This seems small to me, but I can't see any glaring flaws in logic/calculation, so I'll come back to it later if I need to.
Commercial: I am using this to include shops, malls, office buildings, schools, churches, etc. On a standard day in the afternoon, I'm going to assume that about half of all people in the U.S. (roughly 150,000,000 people) are in these types of structures. Based on anecdotal experience and very rough estimates on order of magnitude, I'd say every one of those people averages 50-100 square meters of space to themselves. However, that does not include all of the empty spaces (closets, storage, parking decks, churches during the week, etc.). Adding that space in, let's say 200 square meters per person. However, the average commercial space has more than one story (let's assume 2 average), so we have to divide the total by 2. This gives us a total of 15,000,000,000 square meters, or 15 square kilometers. Again, this seems small, but we can come back to it later.
Industrial: This includes manufacturing plants, warehouses, etc. Top-down, I would say these structures take up about the same amount of room as commercial structures. Bottom-up, there are probably 10,000,000-50,000,000 people in such structures on an average day. However, each of those people probably has 5x more space available to them. Although these are all rough numbers, I think that the order of magnitude is correct: let's assume 15 square kilometers.
So far, I have a total footprint of 40 square kilometers. Assuming I forgot to include a significant number of buildings, let's range the estimate to 50-100 square kilometers. This is obviously tiny compared to my earlier estimate of the size of the United States. Let me do some sanity-checking based on a city I am familiar with.
This city has a downtown area of about 20 square kilometers. I would estimate that about 10% of that is actually covered in structures vs. roads, parks, etc. (2 square kilometers). The metropolitan area is probably about 5,000 square kilometers. However, structure coverage of this area is far, far less on average. I would estimate .01-.1%, for a total coverage of 0.5-5 square kilometers. That puts the total structure coverage of the area at 2.5-7 square kilometers. This metropolitan area is around the 10th largest city in the US and represents about 2% of its population. Multiplying the range by 50 gets us 125-350 square kilometers of structures in the US.
As I thought, the bottom-up estimate came out significantly lower than the top-down. However, they are both around the same order of magnitude. Therefore, my answer to the original question is 0.0005-0.0035%.
All of that being said, I'd like to apologize for the absurd length of this post.
2 quick questions about this part:
1) Why divide the total by 2? Why does it matter in terms of how much space it takes up? 2) Isn't 15 B square meters=15,000 square kilometers? 150 B square meters x 10^-6= 15,000.
1) If a house is 2,000 sq ft but has 2 floors, it only actually takes up 1,000 sq ft of space (its footprint) 2) Yes, you're absolute right; this is where I went wrong (I was, for some reason, imagining that square kilometers were cubed). Good catch. That makes me question the order of magnitude of the two commercial and industrial numbers.
The good news for me is that most interviewers really are only interested in the process. The fact that I made a pretty simple math mistake really isn't that big of a deal, especially given that the number felt off to me.
tldr ^
Dorsk -- you forgot Alaska.
The continental US is about 3.1 million sq miles. So, your estimate was quite good there. Alaska is about 660k sq miles. The total US square miles with Alaska, is actually about 3.8 million. So, like I said, you forgot Alaska.
Just needed to bust your balls a little, so you don't get too cocky.
Absolutely nailed it Dorsk. But yeah, it's only "difficult" if you don't understand the idea behind an estimation question. You don't have to use the same logic or numbers as Dorsk but as long as your numbers stand up to a gut/basic logic check and your thought process makes structured sense, you're "right."
Thanks Dorsk for your detailed response. I feel like OW FS tends to ask these questions whereas other consulting firms tend to focus on more general "how many cars are there in the United States?" types of questions
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