The Hospital Bed Question

THE guesstimate question is a usual type of question that you can expect to be asked when interviewing for a position at a consulting firm.

Here is one to test your mettle.

The Hospital Bed Question

The question is this: How many hospital beds are required in New York city to provide for all of its pregnant women? 

You can assume that:

  1. pregnant women stay in hospital for one night only (American hospitals are very expensive); and
  2. hospital beds in New York are used exclusively by New York residents (no sharing).

If you are game to test your skills, then this is what you need to do.

Please respond in the comments below, covering the following in your answer:

  1. set out the steps that you would take to answer the question;
  2. note any additional assumptions that you would make at each step; and
  3. provide a final numerical guesstimate to the question.

To spice things up, I will be happy to send the best answer (as judged by me) a copy of an interesting book by Lawrence Weinstein (nuclear physicist) and John Adam (professor of mathematics). The book is called Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin.

Note that the comments section remains open for 14 days only, so you have a limited time in which to respond…

Happy guesstimating.

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.

12 Tips for Nailing the Guesstimate Question

AS WE found out in the previous post, the guesstimate question is a usual type of question that you can expect to be asked when interviewing for a position at a consulting firm.

Here are 12 tips to help you nail the guesstimate question:

  1. Practice: We live in a world where most of us use a calculator or computer every day and it can be easy to forget how to do basic arithmetic in your head. Practice doing some guesstimate questions before the interview so that you are prepared. It is a good idea to bring a pen and paper to the interview to keep track of your calculations.  The Vault.com has also suggested bringing graph paper to the interview so that you can graph your results.
  2. Know some basic facts: It will help to know a few basic facts to give you a starting point from which to make reasonable assumptions. It is a good idea to know some key country and city population estimates.  For example, estimates for the population of the world (7 billion), America (300 million), Australia (20 million), New York (20 million), Sydney (4 million) and Melbourne (4 million).
  3. Use round numbers: You are responsible for doing the calculations so pick numbers that are easy to work with. For example, estimate the population of America as 300 million not 309.3 million.
  4. Get into character: An easy way to calm your nerves and improve your performance is to role play. You are not a university graduate desperate for a consulting job, you are a professional consultant. Game on!
  5. Take a moment: It is important to maintain your composure so before starting to answer the guesstimate question take a moment to consider your approach. You can buy yourself some time by saying, “That’s an interesting question” and then pausing to think.
  6. Have a clear approach: It is important to have a clear approach to help you answer the question.
  7. Ask questions: Your interviewer may be able to provide you with direction. If the question is “How many ping-pong balls will fit inside a 747?” the first question you might want to ask your interviewer is “What is the volume of a ping-pong ball?”
  8. State your assumptions: The interviewer may not know the answer or may not want to give you direction so you’ll have to make assumptions.  It is a good idea to clearly state your assumptions. For example, “let’s assume that the diameter of a ping-pong ball is 4cm. The formula for the volume of a sphere is 4/3.pi-r^3. The volume of a ping-pong ball would therefore be about 11-pi centimetres cubed”.
  9. Think out loud: The interviewer is trying to assess your thought process in getting to the answer, not the answer itself. If you don’t think out loud, you make it difficult for the interviewer to give you points.
  10. Explain your logic: As you make your way through the problem it is helpful to explain the logic behind each of your assumptions. Instead of saying “a 747 is about 100 metres long” you could say “I know that  an average car is about 5 metres long and based on my experience I would say that 20 cars lined up end to end would be about the same length as a 747. So I will assume that a 747 is 100 metres long”.
  11. Answer the question: After doing all of the calculation remember to answer the question that has been asked.
  12. Be prepared for the follow-up question: After you answer the guesstimate question, you may be asked “If you had to find the real answer to the question, how would you do it?” This is a test of your creativity and resourcefulness.

The Guesstimate Question

THE guesstimate question is a usual type of question that you can expect to be asked when interviewing for a position at a consulting firm.

What will you be asked to do

A typical guesstimate question will require you to estimate a number by doing a rough “back of the beer coaster” calculation. You are supposed to reach a final answer by using a series of narrowing assumptions.

Your assumptions should have a sound basis and you should explain the logic behind your assumptions, however it is not important that your assumptions be 100% accurate.

What is being assessed

Your response to the guesstimate question will help the interviewer evaluate your strengths in the following areas:

  1. professionalism and ability to remain level-headed when placed in a tricky situation;
  2. creativity and sound judgement in being able to come up with plausible assumptions;
  3. logic and structured thinking; and
  4. numerical skills and level of comfort with doing basic arithmetic in your head.

The guesstimate question is quite different from the kind of interview questions that you are probably used to.  For the guesstimate question, it is better to arrive at the wrong answer with good assumptions and clear logic than to know the right answer because you saw it on the Discovery Channel last week.

Examples

Here is a list of example guesstimate questions to give you an idea of the kind of questions to expect:

  1. How many births are there in America each day?
  2. How many petrol stations are there in Sydney?
  3. How many bottles of wine are consumed in France each month?
  4. How many cups of tea are drunk in England each day?
  5. How far does the average Premiership footballer run in a single game?
  6. How much does Mount Kilimanjaro weigh?
  7. How many pounds are spent on haircuts in the UK each year?
  8. How many ping-pong balls will fit inside a 747?
  9. How many weddings are performed in China each year?
  10. How many men’s suits were sold in the United States last year?
  11. How many tennis balls fit in a swimming pool?
  12. What is the annual size of the golf ball market in Japan?
  13. Estimate the total revenues obtained from the movie Avatar.
  14. What is the size of the market for mobile phones in America?
  15. How many white cars are there in Australia?
  16. How many people are buried each year in England?
  17. What is the annual market for apples in America?
  18. What is the annual revenue of Harrods in London?
  19. What is the market for bicycles in America?
  20. How many taxis are there in New York?