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by Vault Careers | January 06, 2021


Guesstimates such as How many ping-pong balls fit in a 747? are among the most unnerving interview questions you can receive. They can seem so off the wall that they can shake up even the most calm, collected candidate. In fact, that’s exactly the reaction interviewers are expecting. The main objective of these questions is to evaluate your poise and professionalism when facing an outlandish situation. How you react to guesstimates can speak volumes about your ability to be professional when faced with difficult business situations.

The good news is if you know how to approach answering guesstimate questions, they won’t throw you off at all—and can even be enjoyable, like puzzles are enjoyable. Below are the necessary tactics for answering these questions, using the example about ping-pong balls in a 747—an actual question used in consulting interviews—as a model.

1. Don’t panic

When approaching a guesstimate question, the first thing to remember is not to panic. If you’re visibly shaken when presented with a guesstimate, it’ll hurt your candidacy—it’s extremely important that you don’t lose your cool. Also, don’t let yourself struggle verbally. You’re free to say something like, “That’s an intriguing question. Can I have a moment to think it through?” This statement immediately shows your interviewer that you’re still in control and gives you some breathing time to think about a method for answering.

2. Think out loud

When answering a guesstimate, you want showcase your ability to analyze a situation and form conclusions by thinking out loud. You’ll drive toward a conclusion through a series of increasingly specific analyses. Once you’ve had a minute to compose your thoughts, be sure to talk through your reasoning, allowing your interviewer to see (and hear) that you're arriving at your answer in a logical manner.

3. Round up and estimate

“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 1 million, and you can divide by 350, instead of 365, if you need to divide by the number of days in the year.” That is, remember that you choose the numbers, so pick nice round numbers that are easy to manipulate. Even if you just read a study that says there are 316 million inhabitants in the U.S., no interviewer will flinch if you estimate the number of American inhabitants as 300 million. The logic that you use to derive an answer from your assumptions is much more important than the perfect accuracy of the assumptions themselves.

4. Think of a funnel

When it comes to analyzing the guesstimate, the best approach is to think of a funnel. You begin by thinking broadly, then slowly narrowing down towards an answer. So, first, you have to locate the tip of the funnel. In the ping-pong ball question, when you’re looking for how many balls fit in a 747 airplane, your starting point is this: the volume of a ping-pong ball.

5. Ask questions or make assumptions

For any guesstimate, if assumptions are fairly easy to make, then don’t ask your interviewer questions. If assumptions are difficult to make, or you run into difficulty assuming anything, then questions are okay to pose. In the ping-pong example, it seems fairly easy to estimate the ball’s volume. So, it’s likely unnecessary to ask: “What’s the volume of a single ping-pong ball?” In the case of this guesstimate, your verbal response/reasoning—and the beginning of your answer—might go something like this: Let's assume that the volume of a ping-pong ball is about three cubic inches.

6. Don’t be afraid to ask for pen and paper

No one expects you to be a human calculator, so even if you’re estimating and rounding, you certainly can 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.

7. Put it altogether

Now that you understand the basic guidelines of how to answer a guesstimate, you’re ready to put your knowledge into practice. As an example of a good answer, here’s how the rest of an acceptable answer to the ping-pong ball guesstimate would go (let’s assume the answerer has pen and paper and is doing the math as she goes).

Next, let's assume that all the seats in the plane are removed. We'll say the average person is 6 feet high, 1 foot wide, and 1 foot deep. That's 6 cubic feet. Since 1 cubic foot is 1,728 cubic inches (12 x 12 x 12 inches), a person has a volume of about 10,368 cubic inches (6 x 1,728 cubic inches).

Next, let’s assume a 747 has about 425 seats—400 on the bottom deck and 25 on the top deck. Then let’s assume there are 3 galleys, 14 lavatories, and 3 aisles (2 on the lower deck and I on the upper deck). We’ll assume the space occupied by the galleys is a 6 person-equivalent, the space by the lavatories is a 2 person-equivalent, and the space by 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 person-equivalents for the galleys, 28 person-equivalents for the lavatories, and 120 person-equivalents for the aisles, or a subtotal of 166 person-equivalents of extra space. We won't include the cockpit in the estimation, because someone has to fly the plane full of balls!

So, in all, there are about 600 person-equivalents available. [You could round a bit to make your life easier, because the actual number is 591 person-equivalents (425 + 166).]

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' heads. 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. [It's not too important that this assumption be correct, just that you know the assumption should be made.]

Therefore, in total, we have 3,000 (600 + 2,400) person-equivalents in volume available. 3,000 person-equivalents x 10,368 cubic inches (the approximate volume of a person) equals 31,104,000 cubic inches of space available. So, at three cubic inches per ball, a 747 could hold 10,368,000 balls (31,104,000 divided by 3).

However, spheres don’t fit perfectly together. So if we eliminate a certain percentage—let’s assume spheres cover only about 70 percent of a cube when packed—we cut the answer by 30 percent and get a grand total of 7,257,600 balls.

This post was adapted from the new Vault Guide to Case Interviews.