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Guesstimation Interview Questions

Posted by James M on December 9, 2008

Guesstimation interview questions are in the same family as logic questions and require a similar type of response framework.  They are used primarily in the high tech and consulting industries.  In this post I’ll try and tackle one of the most famous of these questions: How much does Mount Kilimanjaro weigh?  Remember, these are not trivia questions, but rather questions used to test your ability to make assumptions, simplify complex problems, and maintain a logical framework to problem solving.

Before you waste your time reading my ramblings, you might consider viewing this video from Vault.com.  It approaches this type of question from a sample interview point of view, and gives some very helpful tips.

Thanks Vault!!  Now I’ll try to tackle the Mount Kilimanjaro question with an analysis provided below. I’ve written my equations in numerical values instead of writing them out in English for clarity and simplicity while reading.

How much does Mount Kilimanjaro weigh?

“Oh, wow, a lot?  Ok, well I think I have seen pictures of the mountain and I remember it is suppose to be pretty tall, maybe like 15,000 feet.  So I guess let’s assume it is 15,000 feet tall.  And in the pictures I seem to remember it was pretty wide, it looked wider than it was tall, so maybe it is 20,000 feet from end to end along the base. So to figure out how much it weighs I just need to figure out the volume and then figure out how much that volume weighs.  So I’ll do the calculation in cubic feet and then just multiply by the weight of one cubic foot of rock.

So to make the calculation manageable lets assume the mountain is a perfect cone, basically a cone with these dimensions I wrote down—a radius of 10,000 feet and height of 15,000 feet.  So, let me think.  The formula for a cone is…(1/3)pi*(r^2)*h.  So let’s see r^2 is 10,000^2 which is 100 million feet.  100 million times the height of 15,000 feet is 1.5 trillion feet.  So 1/3 of that is 500 billion.  So 500 billion*pi feet cubed is the mountain’s volume.  Ok, how much does rock weigh?  I remember I helped my dad build a small stone wall by our old house a few years ago, and the rocks were about a foot square and six inches deep.  So that is half the size of a cubic food.  I think they probably weighed about 70 Ibs.  So I can assume the weight of 1 cubic foot of rock is about twice as much, so that would be 140 pounds.  So 140 which is the weight of one cubic foot of rock times 500 billion*pi which is the volume of the mountain is 7X10^13 pi Ibs.  Wow, that is a lot.”

Analysis
So, there are really there components to answering this type of question involving math and estimation.  First, you need to be able to make reasonable assumptions.  Making assumptions is part of any job especially engineering—you have to simplify tasks into manageable parts which involves assumptions.  So if you say the density of rock is 12 Ibs per cubic meter or that Mount Kilimanjaro is 5 miles high, this might indicate to the recruiter that you will have trouble creating grounded assumptions.  Again, the best way to make assumptions is to use reference points.  For example, I mentioned the photo of the mountain I remembered seeing and the stone wall I helped my dad build.

Second, you should be able to do the basic math involved in these sorts of problems.  Yes, the numbers were big in this example, but they involved lots of zeros so it really wasn’t that hard.  In addition, you’ll have scratch paper during the interview.

Third, and most importantly you need to have a chain of logic.  Again, it is not the right answer that is important, but how you talk through distilling the problem to its essence and the steps you go through to get to the answer as you describe it in your opening problem statement.  In reality Mount Kilimanjaro is 19,340 ft and the density of rock is more like 167 Ibs per square foot, but since this isn’t trivia, but about problem solving, the assumptions we made will do just fine.

Well that’s all for today.  If you have any questions or would like free resume consulting, feel free to e-mail me at collegegraduatejobs@gmail.com.  Thanks for reading!

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