After a meeting with your client, they say: “So you are saying the market I am playing in is worth $50 million and that it has been growing at 5% a year. That’s really interesting. Do we know how big it will be in five years?”
There you are, on the spot. One of the main reasons McKinsey tests your maths skills in the PST is that clients will test your maths skills in real life by asking unexpected questions. This can happen in a lot of situations, from a working session with a junior client to a board meeting at the end of a project. Clients will react to what you say with follow-up questions that sometimes involve maths.
Your first challenge when preparing for the McKinsey PST is to do the maths right. Your second and most important challenge is to do the maths quickly.
At some point in our life we have all known how to do the maths right. But those of us who have not used quantitative skills in a while will probably be a bit rusty when going through a long-division for the first time since high school.
Your second and most important challenge is to do the maths quickly. Whereas it seems a few people are just gifted in maths and blast through calculations in the blink of an eye, a lot of us are not. The good news is there are a few things you can do and learn to increase your maths speed dramatically.
Your maths speed depends on two things: how much you have trained and how good your technique is. It doesn’t matter how hard she trains, the performance of an Olympic rower will probably depend on how good her technique is. Mental maths is no different to rowing. To do it well and fast, you have to have the right technique and train hard.
However, when taking the McKinsey PST, being fast is not about mental maths “tricks” and “tips”. It’s about approaching and tackling each question in the right way.
1. The 10% rule
When faced with a quantitative PST question, the first thing you need to ask yourself is: “Is this a precise maths question or is this an estimate maths question?” This is a very important question, and probably one of the most important ones you should ask yourself during the test. This is crucial because if you answer an estimate maths question by doing precise calculations you will lose a lot of time unnecessarily.
You need to develop your ability to quickly identify if a question requires you to make estimates or to compute precise calculations. In our experience, this is best achieved by looking at the answers of the question you are trying to tackle. Here is the approach we recommend.
If the numerical answers of the question are within about 10% or less of each other, you probably need to go through precise calculations. If this is not the case, you are probably better off going down the estimation path.
2. The lazy rule
Once you know if you are dealing with a precise maths question or an estimate maths question, the following step you need to go through is to identify which calculations you are going to do. We recommend that you take a few seconds to mentally plan your calculations.
When you do this, your objective should be to minimise the number of calculations you are going to do. In other words, be as lazy as possible. Investing five seconds to think about this will often save you 30 seconds spent on a calculation you could have avoided. Saving this time could allow you to answer that extra question at the last minute that will make you pass the test.
In our experience, planning your calculations is particularly valuable in the following two cases:
- When you need to go through more than three calculations steps to get to an answer. In these cases, you will often find that there are two or more ways to get to the right option. Take a second to plan your approach before diving into computations.
- When the question you are trying to answer involves ranking a series of options. For instance, if you have to rank four companies in terms of their profit per employee, from the highest to the lowest, you will often find that you do not need to calculate the profit per employee for all four companies. Instead, by doing two or three calculations you will often be able to pick the right answer by eliminating the other options.
3. The growth rule
Calculating growth rates over multiple time periods is technically feasible by hand; however it is extremely time consuming. If a $50 million market is growing at 5% per year for five years, you need to do the following computation to calculate the five years compounded growth rate:
(1 + 0.05) x (1 + 0.05) x (1 + 0.05) x (1 + 0.05) x (1 + 0.05) = 1.27 – or 27% growth over the five year period
Doing this would likely take you more than two minutes which you probably cannot afford when taking the McKinsey PST. Instead, we recommend that you use the following shortcut.
By multiplying the yearly growth rate and the number of years during which it will apply you can get a good estimate of the compounded growth rate you need to answer the question. In our example you would do the following calculation:
5% per year x 5 years = 25% growth over five years
Doing this would probably take you less than ten seconds and therefore save you a lot of time. There are a few things you need to be aware of when using this technique.
First, when using it with positive growth rates, it will underestimate the compounded growth rate. In this case, the shortcut gives us 25% versus 27% for the precise calculation. In most cases, this degree of precision should be sufficient. Conversely, when using it with negative growth rates, it will overestimate the compounded growth rate.
Then, you should also be aware that the higher the yearly growth rate and the number of years to which you are applying it to, the less precise this technique becomes. For instance, 10 years of growth at 10% per year corresponds to a 160% compounded growth while our shortcut would give us a compounded growth of 100% (10% per year x 10 years).
We therefore recommend that you become familiar with this technique and use it with caution when working on long periods of time and high growth rates.
Take the time to learn and practice these three approaches; they will save you invaluable time. By applying them consistently your speed at tackling maths PST questions will almost undoubtedly improve. Once you have absorbed these techniques, you might even be able to answer this McKinsey PST question in less than 30 seconds!
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Any questions about the McKinsey PST?
If you have any questions about the McKinsey PST, do not hesitate to ask them below and we will be more than happy to answer them. All questions are good questions, so go ahead!
The IGotAnOffer team
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