Guesstimates are fast becoming a sought after tool for employers and their effectiveness comes as no surprise given the fact that this technique can closely assess candidates on the basis of some very crucial skills such as:

• Ability to make quick checks on the efficiency of different methods or approaches
• Ability to make reasonable assumptions
• Ability to do back-of-the-envelope calculations
• Ability to think on your feet
• Ability to be structured with limited or no data at hand
• Ability to perform under pressure
• General knowledge, awareness & common sense

Estimation problems can really throw candidates off and might seem impossible – especially under the time pressure of an interview. However, there really is no reason to panic. Estimations are generally quite straightforward when approached correctly. A systematic and thoughtful approach will take you a long way to very plausible estimates of seemingly impossible quantities. The following steps can help you do that:

Ask Preliminary Questions

As soon as you hear the guesstimate problem, your first response should be to ask reasonable preliminary or clarifying questions. Asking good preliminary questions will help you to define the scope of the problem and establish boundaries. Without limiting the scope of the problem, you might feel overwhelmed with the amount of work that you have to do in order to crack the guesstimate problem.

Make Assumptions

An assumption is something that you assume to be the case, even without proof. For example, people might make the assumption that you’re a nerd if you wear glasses, even though that’s not true.

Most of the problems that we face in our everyday lives are ill-defined to some degree. For example, what to do for your child’s birthday party, what to cook for supper, and how to ensure that you will have a continuous and plentiful supply of drinking water are all, in varying degrees, ill-defined problems. A main difference between well-defined and ill-defined problems is the degree to which they are constrained. A problem’s constraints can determine what information and materials are pertinent to the problem, and what operations are allowed in solving the problem. A standard technique used to solve ill-defined problems is to make subjective assumptions that can make it “more” defined, limit the size of its solution space and turn it into a well defined problem.

Break Down into Smaller Parts

This is the most critical part of solving a guesstimate question and it’s important that you ‘take a moment’ to think about how to go about it. Thirty seconds of silence now may save wasted time later in the interview. Remember that there are often multiple ways to break down a problem. You should pick the one which is logical and which you feel the most confident about.

You might find yourself thinking pictorial at this point. Don’t hesitate to use a paper and pen to draw out a structure and a logical flowchart. In such an eventuality, be confident to share your work with the interviewer. Remember that guesstimate problems are back of the napkin calculations so they needn’t be unnecessarily long and subjective.

Breaking down the problem into smaller components helps you to focus on one small problem at a time which is easier to handle as compared to cracking the entire problem in one go. It also gives you the flexibility to revisit and correct a small part of your calculations if you think you have made a mistake, rather than redo all calculations from scratch.

Estimation & Calculation

Once you have broken down the bigger problem into smaller, more manageable components, it’s time to feed numbers into your structure. This means estimating each piece using mathematics and background knowledge.

Remember that you have limited time to solve guesstimate questions during an interview. Therefore, it’s very important that you be able to do quick math.

Let’s say, you are asked to:

“Estimate the number of windows in London.”

Your first response should be to clarify what kind of windows in London does the interviewer want you to consider. After all, windows come in various forms. Houses, commercial buildings and apartment buildings, all have windows. This is not all; windows are also found on cars, buses, trains and other vehicles.

Ensuring that you have pin-pointed the exact requirement will save you a lot of time and effort. You don’t want to do a huge amount of work only to realize towards the end that you were required only to calculate the number of windows on cars in London!

Let’s consider another example. Say, you are asked:

“Estimate the number of pizzas that are sold at Dominos every day.”

Here’s a list of some reasonable preliminary questions that you can ask in this case:

• Are we talking of one particular country? Or the global sale of Dominos?
• How many kinds of pizzas are we taking into consideration?
• Am I to consider all kinds of pizzas available on their menu? Or just their best sellers?
• Should I consider dine-in orders only? Or should I also take into consideration the take-away orders?
• How about orders placed using the online mode? Should those be taken into consideration as well?
• Am I to consider Dominos’ outlets at special places like airports? Or are we talking only of typical Dominos’ outlets in cities?

 

Remember that it is worth your time to get a good grip over the Guesstimate problem early on in the game rather than be surprised unpleasantly later on!

So many textbooks are based on well-defined problems that are less complex to solve compared to real world problems which often don’t have definitive boundaries. Therefore, during the recruitment process, panellists challenge candidates to step out of their comfort zones by asking them to crack practical problems that involve making assumptions.

The aim while making assumptions is to simplify the problem at hand. Just remember that the assumptions that are made must be reasonable. For example, if asked about the car sales made in London in one year, a candidate might assume that a typical English household has three members on an average. This might not be accurate but it surely sounds reasonable and useful for calculating the annual car sales. By contrast, assuming that everyone in the United Kingdom holds a driver’s license sounds unreasonable.

Ultimately, you will have to use your own judgement in making assumptions. For example, in order to calculate the car sales in London, if one has already assumed that a typical household in the United Kingdom has three members, then it would be reasonable to further assume that each family owns one car and replaces it every six years.

Listed below are some assumptions which are routinely made while solving Guesstimate problems:

• Even Distribution of Age Brackets
  It can be assumed that there are same number of people in age brackets of the same width i.e. assume that there are same number of people in the age brackets 0-10, 20-30, 30-40……70-80. As an example, if you are asked to estimate the market size of coffee cups that are sold in the U.S., you might say, “I am going to assume a U.S. population of roughly 300 million people divided equally among the 0-20, 20-40, 40-60, and 60-80 age range”. Remember to always justify your assumptions: “I am going to assume we can capture 10 percent market share, because of x and y reasons”.

• Average Lifespan
  It can be assumed that all individuals live for exactly 80 years.

• Market Sizing
  For market sizing interview questions (for example – How many gas stations are there in the U.S?), you’ll be more effective if you have some basic data handy. It’ll save you from asking the interviewer for basic information. The chart shown below can be populated with the most up to date information and used for reference when needed.

	World	Europe	Asia	North America	South America	Africa	China	India	Japan	U.K.
Population
Life Expectancy
People per Household
Median Household Income
GDP
GDP Growth Rate
% Married Adults
% Population Under 18 Years
% Population Over 65 Years

The two most common approaches that you can use to solve guesstimate questions is Top-Down and Bottom-Up/ Ground-Up. In some cases, you may even end up using both approaches.

• Top-Down
  This approach is often used in questions that involve starting from the very top level. For example, solving the guesstimate problem by using the population figure of a country and then breaking it down into smaller components until you arrive at the final answer.Consider the following question:
  “Calculate the number of school teachers in New York” A simple way to approach this question would be to start with the population of New York. In the second step, you may estimate what percentage of New York’s population is students. Then, estimate the number of students per class. Using this, you would arrive at an estimate of the number of school teachers, because generally at any given time there is exactly one teacher per class.Remember that you can always go that extra mile to demonstrate that you are a detail-oriented person by taking into account the retired and substitute teachers as well.
• Bottom-Up/ Ground-Up
  While using this approach to solve guesstimate questions, you often start from the grass root level rather than the top level with a high-level figure such as the population of a country. This could mean using some low-level statistic, such as cost per product, and build your way up to the final answer.Consider the following question:
  “Calculate the monthly revenue of a hair salon in New York” In such a question, you may calculate the revenue made in one day and multiply it by 30. Or, you could also estimate the weekly revenue and multiply it by 4.An assumption can be made for the average price per client visit, and then the weekly volume can be calculated by assuming the number of chairs in the salon, the number of hours it is open per week, and the average number of clients chair per hour.

  Remember that you can always show your skills of creativity and thorough analysis by taking into account the revenue earned by selling hair products at the salon as well. Further on, you may take into consideration the fact that generally female clients spend longer time and more money at hair salons compared to male clients in one visit.

The biggest difference between Mental Math and Academic Math is that in the latter, you are expected to deliver accurate results whereas in the former, answers are often required to be close enough to guide towards the ballpark answer, versus being 100% accurate.

Since the use of calculators is not allowed during interviews, it is crucial to practice and be ready to handle numbers fast, accurately, and without a calculator.

Mental Math Basics

• Rounding numbers

Rounding numbers is always a good idea during guesstimates as it makes your calculations much simpler and faster.

For example,

Approximately 62 million population of the United Kingdom becomes 60 million.

Remember to round the numbers in such a way that doing so does not distort the final answer too much. A good guideline to follow is not to round by more than 10%. It is also helpful to round both up and down as you are working through the problem, so the effects, to some degree, cancel each other out. In the end, also make sure you check if your answer actually makes sense.

Look at another example:

If an answer involves multiplying 44 by 5,300, you will get a more accurate answer with 50 × 5,000 = 250,000 (one rounded up, and the other rounded down) than 40 × 5,000 = 200,000 (both rounded down). (The exact answer is 233,200).

• Dealing with large numbers

It is often cumbersome to deal with large numbers. One strategy to simplify things is to remove all zeros and add them back later. You can also use symbols such as K, M, B to keep track of large numbers.

For example,

300 million can be re-written as 300M and 400,000 can be re-written as 400K. And 20 billion will become 20B.

3 x 50M becomes 3 x 5 = 15 with 7 zeros.

• Break down into smaller parts

Numbers can be broken down into smaller parts for simpler calculations.

For example,

13 x 7 = (10 x 7) + (3 x 7) = 91.

• Subtracting from numbers with 1 followed by zeros

This is also an effective strategy for faster math.

For example,

1000-365 becomes 999-365+1 = 634 + 1 = 635.

• Group numbers into multiple of 10 (addition)

This is another effective strategy for faster math.

For example,

3+7 + 4 + 6 +13 +7 +21 becomes 10 + 10 + 20 + 21 = 61.

Tips to do better Mental Math:

• Don’t forget to seek the interviewer’s permission before rounding up numbers. Almost always you will have his/her permission and that will make mental math calculations much easier and faster.
• Don’t do calculations in haste. Remember that if you make a mistake it will take you even longer to fix it. Of course, there is a lot of time pressure during interviews so do not take any longer than you need. You need to find a good balance. This comes with a lot of practice.
• Don’t hesitate to use pen and paper if you want to. Just make sure that what you write is legible enough for the interviewer to read and understand. The advantage of doing so is that the interviewer might even correct you if your calculations are off or if you are going down the wrong track. But that’s the interviewer’s discretion!
• Keep your writing organized. Let’s say you are estimating how many cars will be purchased in the United Kingdom in 2030. As you are putting down numbers for each element of your equation, keep it neat and organized so you don’t get confused and it will also help you avoid silly mistakes.
• As part of your preparation, refresh key math topics like ratios, fractions, percentages, averages, and probability.

Once you are confident that you have calculated the values of all components, it’s only a matter of carefully integrating the sub-parts and reaching the final answer.

While solving Guesstimate questions, remember the following:

• • • • • Do not assume that you have fully understood what needs to be calculated as soon as you hear the question. Take a few seconds to gather your thoughts and ask preliminary questions.
        • Do not guess the answer as soon as you hear the question. Keep in mind that the interviewer is more interested in hearing your approach towards the problem rather than the end result. The idea is to convince the interviewer that you can think rationally and logically.
        • Do not make assumptions in your head. Making assumptions is an important part of solving the Guesstimate question and it is important that you cross-check them with the interviewer. For example,If asked to calculate the number of hair salons in New York, you could assume that every person in New York gets a hair cut at least once a month. This means that you are not taking into account the small percentage of people in New York who do not get their hair cut at all. It’ll be wise to let the interviewer know of any assumptions you make and ensure that he/she is convinced about them.

• • • • • Do not assume that the interviewer is a mind reader! Remember that you are presenting a solution to someone who cannot read your mind. Therefore, it is very important to keep the interviewer on the same page by sharing your line of thought i.e. your assumptions, approach, logic, break-down of the problem, calculations etc. The advantage of doing so is that you give the interviewer an opportunity to correct you if he/she feels that you are going off track! It’s better to stand corrected earlier in the game than later on.

• • • • • Do not turn each aspect of the problem into an entirely new guesstimate itself! It’s easy to get swayed by your own intelligence and analytical abilities. Focus on simplifying the question and not complicating it.

The following skills are sure to significantly increase your chances of cracking a guesstimate problem and getting another step closer to your goal!

• Structured Thinking

To be able to structure your thoughts lays the edifice for cracking guesstimates. Its value and importance can’t be stressed enough. It is a trait which is highly appreciated by employers.

• Sharp Communication

The three Vs of communication – Voice, Veracity, and Vocabulary when brought into play by you will certainly leave the interviewer impressed and convinced of your good fit for their organization.

• Smart Creativity

Use your creativity in making small assumptions using the things that you observe in your daily life. But don’t forget to be logical!

It can be a little intimidating to solve guesstimates in front of someone for the first time knowing you’re going to be judged, but at the end of the day, it’s like any other interview question, one designed to see what your mental capacity and approach is.