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 are 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.
You choose the numbers, so pick nice round numbers that are easy for you to manipulate. Even if you just read a study that states that there are 270 million inhabitants in the United States, no interviewer will flinch if you estimate the number of American inhabitants as 300 million.
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