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Case study #7: Equator Guesstimate

GradAustralia

You may not realise but the equator may be more relevant to your consulting case interview than you think. Check out our article to find out why.

Case study examples

Case interviews allow you to demonstrate how you think - your ability to understand a problem, break it down into its requisite parts, analyse them and communicate a solution. In this series, we give you ten case studies to give you an idea of how to approach the case and how to walk through it with your interviewer.

You may want to consider the case question first and think about how you might structure a response before looking at the ‘answer’. Of course, bear in mind there are many ways to answer a case, so this is just one example!

For the purposes of these examples, we will only look at market sizing and business cases.

Case study #7: Equator Guesstimate

Question

How many pages of paper would it take to completely encircle the earth at the equator?

Solution

This is a tricky question to conceptualise at first hearing but rest assured, as we break it down, it becomes much more straightforward. It is ok to admit that you don’t have the answer straight off the bat or that this is an area that you are not familiar with. Let’s have a go.

You: That’s a good question! I have to admit, I don’t know a lot about the size of the earth but I’ll talk you through my thinking as we go along.

Interviewer: Ok great.

You: Perhaps we can start with the paper. I do know that a standard A4 piece of paper is about 20 cm by 30 cm give or take. I’m going to assume that the easiest way to think about this is by using the paper lengthwise, so at 30 cm.

Interviewer: That is a solid assumption. Let’s go with that.

You: Next, we have to consider the size of the earth. Hmm, well I have travelled a lot between Sydney to Perth and I’m sure the distance between them is roughly 3,000 km. I’m going to assume this is right if that’s ok with you.

Interviewer: Actually I think Sydney to Perth is almost 4,000 km…

You: Ok no problem. Let’s say 4,000 km then. I have looked at the size of Australia on a globe before and it is quite a large continent. While it isn’t the largest country in the world, I would say that you could probably fit about ten Australia’s around the centre of the earth at least.

That would imply say about 4,000 * 10 = 40,000 km is roughly the distance around the earth at the equator. 40,000 km is the same as 40 million metres and 40 billion cms! And if each A4 piece of paper is 30 cm lengthwise, then that means we would need 1.3 billion pieces of A4 paper. That sounds quite outrageous!

Interviewer: Are you happy sticking with this estimate?

You: Well, another way to sanity check this would be to check the distance of the equator, assuming that my maths is correct. The 40,000 km figure feels about right but I might look at it a different way. I’m pretty comfortable with the 4,000 km spanning Australia, and I know that it takes a few hours to fly from Sydney to Perth. That feels about right because I remember reading somewhere that 747s fly about 1,000 km per hour.

Maybe I can use those numbers to check my figures. During uni, I bought a round the world ticket. I think that the distance between LA to NYC is about the same as Sydney to Perth, that is about 4,000 km. I know that from LA to Tokyo, it’s about eight hours, so let’s call that about 8,000 km.

So now I’m at about 12,000 km from New York to Tokyo. From Tokyo, I’ll go across to Russia. I have no idea what the flying time is but I know it’s long. I think Russia is the world’s biggest country actually. So I’m going to say it’s about three times bigger than Australia and the US. This means it is about 12,000 km across. Now, I’m at 24,000 km from New York to the Ural Mountains.

I haven’t flown across Europe before, but say the EU is similar in size and population to the US, then maybe we can say it is also about 4,000 km across. That might be a bit high but let’s roll with that for the moment. This brings me to about 28,000 km. Plus, then I fly from say London back to NYC. The flight time for this is about five hours, so let’s say another 5, 000. This brings me to 33,000.

I’ve been flying across the world in the Northern Hemisphere but we’re talking about the equator so the distance must be even greater. So let’s tack on a few more kilometres, which brings it closer to the 40,000 km of my original estimate.

Interviewer: I like the way you think. Let’s move on to the next part of the interview.