Guesstimate Case Interviews

Guesstimate questions are among the most unnerving questions you may ever have to answer in an interview situation. They can be so "off the wall" as to shake up an otherwise calm, collected candidate.

The approach to guesstimates is basically the same as business cases -- you will showcase your ability to analyze a situation and form conclusions about this situation by thinking out loud. The difference here is that you will not necessarily be using a series of questions to gather feedback from the interviewer. Instead, you will drive toward a conclusion through a series of increasingly specific analyses. Let's look at an example:How many ping-pong balls fit in a 747?

This is an actual question used in consulting interviews. If you are a little unsettled by this type of question, it's no wonder. That is exactly the reaction the interviewer is expecting. Remember that the main objective of these questions is to evaluate your poise and professionalism when facing an outlandish situation. How you react to this question when presented will speak volumes about your ability to be professional when faced with a similar business situation at a client.

So, how do you approach a guesstimate question? First, don't panic. If you are visibly shaken when presented with a guesstimate or brainteaser, it will hurt you. It is extremely important that you do not lose your cool.

Do not let yourself struggle verbally. You are free to say something like, "That is an intriguing question. May I have a moment to think it through?" This statement immediately shows the interviewer you are still in control and gives you some breathing time to think about a method for answering.

Once you have had a minute to compose your thoughts, be sure and go through your reasoning out loud, so your interviewer can see that you're arriving at your answer in a logical manner. "Don't be anal," suggests one former consultant. "You should realize that for the purposes of a guesstimate, 1,000,553 is the same as a million, and you can divide by 350 if you need to divide by the number of days in the year."

Finally, remember that there is no right answer for guesstimates. It will often not even be necessary to come up with a definitive response like "1,400,350," due to constraints on time. Always work toward a final answer, but do not feel that you have done a poor job if the interviewer moves on to other topics before you are finished. They may simply recognize that you're on the right track and see no reason to keep going.

Acing Guesstimates

The best approach for a guesstimate or brainteaser question is to think of a funnel. You begin by thinking broadly, then slowly drill down towards the answer. Let's look at this approach in context. Referring to our sample question, you know that you are looking for how many ping-pong balls fit in a 747 airplane. The first thing you need to determine is the volume of the ping-pong ball.

For any guesstimate or brainteaser question you will need to understand whether your interviewer will be providing any direction or whether you will have to make assumptions. Therefore, begin the analysis of a guesstimate or brainteaser question with a question to your interviewer, such as, "What is the volume of a single ping pong ball?" If the interviewer does not know or refuses to provide any answer, then you will know that you must assume the answer. If the interviewer does provide the information, then your approach will be a series of questions. For this example let's assume your interviewer wants you to make the assumptions. Your verbal dialogue might go something like this:

Let's assume that the volume of a ping-pong ball is three cubic inches. Now let's assume that all the seats in the plane are removed. We'll say the average person is six feet high, one foot wide and one foot deep. That's 6 cubic feet, or 10,368 cubic inches. (One cubic foot is 12x12x12 inches, or 1,728 cubic inches.)

Okay, so a 747 has about 400 seats in it, excluding the galleys, lavatories, and aisles on the lower deck and about 25 seats on the upper deck. Let's assume there are three galleys, 14 lavatories, and three aisles (two on the lower deck and one on the upper deck), and that the space occupied by the galleys is a six-person equivalent, by the lavatories is a two-person equivalent, and the aisles is a 50-person equivalent on the lower deck and a 20-person equivalent on the upper deck. That's an additional 18, 28, and 120 person-volumes for the remaining space. We won't include the cockpit since someone has to fly the plane. So there are about 600 person-equivalents available. (You would be rounding a bit to make your life easier, since the actual number is 591 person equivalents.)In addition to the human volume, we have to take into account all the cargo and extra space the belly holds, the overhead luggage compartments, and the space over the passengers' head. Let's assume the plane holds four times the amount of extra space as it does people, so that would mean extra space is 2,400 person-equivalents in volume. (Obviously, this assumption is the most important factor in this guesstimate. Remember that it's not important that this assumption be correct, just that you know the assumption should be made.)

Therefore, in total we have 3,000 (or 600 + 2,400) person-equivalents in volume available. Three thousand x 10,368 cubic inches means we have 31,104,000 cubic inches of space available. At three cubic inches per ball, a 747 could hold 10,368,000 balls. However, spheres do not fit perfectly together. Eliminate a certain percentage spheres cover only about 70 percent of a cube when packed and cut your answer to 7,257,600 balls.

You might be wondering how you would calculate all these numbers in your head! No one expects you to be a human calculator, so you should be writing down these numbers as you develop them. Then you can do the math on paper, in front of the interviewer, which will further demonstrate your analytical abilities.