Take a pragmatic approach when working with numbers

Strike a balance between pragmatism and accuracy. Round up numbers/work with averages when necessary to ensure you can make calculations mentally if required. Perhaps round some numbers up and some down in order to ensure you remain as accurate as possible. For instance, instead of including 19% in your calculations, round it up to 20% for the sake of simplifying the calculations, and instead of taking 58 million as a size of the population, round it up to 60 million (again remember that it is not the final number that matters).

If the interviewer will let you, validate your proposed process of reaching a conclusion with the interviewer before plugging in your estimations. You could also see if the interviewer is willing to validate your estimations along the way, as if the interviewer feels your estimations are fair, at least you know you are along the right track. 

A majorly inaccurate estimation at the beginning of a set of calculations could completely diminish the accuracy of your final figure, even if a majority of the subsequent estimations are realistic. On that note, consistently stop to sanity check your figures, as this can help to ensure that your estimations are leading you towards a conclusion that is not wholly illogical.

Sanity check: once you have made a few estimations and started to make calculations, performing a ‘sanity check’ means assessing whether the results of those calculations vaguely relate to the figure that common sense would dictate could be correct. A sanity check could, for instance, indicate that you have missed a zero along the way, or massively overestimated or underestimated the size of the market or its specific segment.

When you first arrive at a final number, you should use your business judgement to determine whether that number is realistic. Your intuition should tell you whether the number seems either too big or too small. You should then be able to verify your assumptions, identify those that may have led to the final under/over-estimation, and consider whether more appropriate estimations can replace any of your existing estimations in order to give you a more realistic and logical final number. Once you have corrected and restated your assumptions to the interviewer, you may then be asked to perform the calculations again.

Break down case study questions into smaller problems

One way to approach market-sizing questions is to first break the question down into a series of little problems, then note down your various estimates within a broader "tree" (i.e. flowchart-style framework). If you have 20 minutes to solve a problem, do not make a couple of rushed calculations and give your estimation within the first 2 minutes. The more time you have, the more you should try to break down the overarching case study and demonstrate to the interviewer that you are able to think flexibly, make informed assumptions, and recognise and consider a wide range of variables. 

Consider a broad range of variables

For example, if you are asked how many chocolate bars are purchased in England annually, remember to take into account chocolate bars purchased by tourists within the UK rather than simply estimating the proportion of the English population that purchases chocolate bars. If asked how many jackets Tesco sells annually, consider the proportion of Tesco stores that sell clothing. If asked how many cars are sold by BMW in the UK every year, does this mean only cars branded with the BMW logo, or other cars produced by BMW (for instance, Minis)? 

Key considerations when making assumptions

Only make assumptions for the following reasons: 

1. To very briefly demonstrate that you are considering every detail; or 

2. If they really do help you to answer the question. 

To place this advice in context, let’s consider the assumptions made in relation to the Wembley Stadium example set out later in this chapter. The assumption that the stadium is set up for football match demonstrated that I am able to consider a variety of variables that could impact on the answer and make a reasonable judgment call. The decision to treat the stadium as if it were a cuboid and treating footballs as cubes enabled me to reach a final answer (based on the various estimations made) using fairly simple arithmetic. 

Using sensible estimations and simple calculations

Whilst assumptions relate more to the conditions you adopt and the logic you follow when considering a particular question, estimations are used to come up with values that you can then input into calculations. Try not to make blind (i.e. random/ill considered) estimations. Justify as many of the estimations/assumptions in your answer as possible. The only way you are likely to fall down when making estimations is if your estimations are clearly unfounded (e.g. estimating that a football pitch is 20 metres long). 

Using a pen and paper can also help you when making more complicated calculations. You must try to find a balance between being detailed in your logic and estimations and using numbers that you will be able to deal with comfortably under pressure. 

You may have to do calculations without a calculator during an assessment day. Where this is the case, consider ensuring that the numbers you estimate are fairly easy to deal with and/or practise making complex calculations without a calculator beforehand. Consider these two examples:

• Instead of trying to divide the volume of the stadium by 0.008 metres³ (the estimated volume of a football), you could round up the size of a football to 0.01 metres³. This would make the division easier to calculate in your head under pressure. 
• When trying to calculate the volume of the stadium based on the estimated dimensions (300m x 270m x 50m) you could break down the calculation into more digestible stages. Start by removing the four 0s, leaving you with 3 x 27 x 5. Next, (if needed) break this down further. 3 x 27 = 81, so we need to calculate 81 x 5. 81 x 5 can be broken down as follows: 8 x 5 = 40, so 80 x 5 = 400 → 81 x 5 = 405. Finally, you add back the four 0s (i.e. multiply by a factor of 10,000) that you originally removed, leaving you with 4,050,000. 

You can sometimes draw on logic based on similar or analogous scenarios 

If asked about a hypothetical market, you could start by considering which industries already provide for a similar end-goal. For instance, if asked what the potential market for teleportation would be, you could consider the current market for long-haul flights as your starting point (as both teleportation and long-haul flights relate to people wanting to travel). You could then base your estimates on the market for long-haul flights, whilst acknowledging that factors such as price, accessibility and safety would impact upon the estimations.