Approaching the Guesstimate Question

IN A RECENT post we learnt 12 tips for nailing the Guesstimate Question, which is a usual type of question that you can expect to be asked when interviewing for a position at a consulting firm. We now consider how to approach the Guesstimate Question.

There are at least three ways to answer a guesstimate question:

1. Try to guess the answer;
2. If you can’t guess, break the question down into smaller pieces that you can guess; or
3. If you still can’t guess, establish possible upper and lower bounds within which the answer is likely to fall.

1. Guess the answer

In the case interview the “try and guess” approach is unlikely to be helpful because the guesstimate question is unlikely to be straight forward. For example, you could be asked “How many tennis balls fit in a swimming pool?” There is no way you can guess the answer to this question, and the interviewer will not be impressed if you try. The interviewer wants to assess your logic and creativity in arriving at the answer.  You will need to break the question down into smaller pieces.

2. Break the question down into smaller pieces

You can break the question down into smaller pieces by asking the interviewer questions. And if the interviewer doesn’t have an answer, you can make a series of narrowing assumptions.

a) What is the volume of a tennis ball? “Assume 140 cubic centimeters.”

b) Are we talking about a standard Olympic sized swimming pooling? “Yes.”

c) What is the volume of an Olympic swimming pooling? “What do you think?”  You will need to make a series of narrowing assumptions and might reason as follows:

I know that an Olympic swimming pool is 50 meters long.

An Olympic swimming pool has 8 lanes and, based on my experience, each lane is about 2.5 meters wide. So, I will assume that an Olympic swimming pool is 25 metres wide.

Based on my experience, an Olympic swimming pool is about 2 meters deep at the shallow end and 3 meters deep at the deep end. I will assume that the pool starts getting deeper at the 30 meter mark and hits maximum depth 10 meters from the end of the pool.

d) What is the volume of a tennis ball in cubic metres?

e) How many tennis balls fit in a swimming pool?

3. Establish upper and lower bounds

Establishing possible upper and lower bounds for an answer is a good way to sanity check that the final answer is in the right ball park.

The number of tennis balls that fit inside an Olympic sized swimming pool is almost certainly more than 10,000 and less than 100,000,000. Therefore, our initial estimate is in the right ball park.

4. Take the extra step

Since tennis balls are spherical, there will be small gaps between the tennis balls. This means that the actual number of tennis balls that fit in an Olympic swimming pool will be less than our initial estimate. Let’s assume that 5% of the pool is filled by the empty space between tennis balls.

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