This is the ninth theory session of the Problem Solving Test Course. I explain most common caveats (traps) of the test and show on examples how to avoid them:
00:20 Example 01
04:00 Caveat 01 – Whole vs Part of Whole
05:06 Caveat 02 – Absolute value vs % Share
05:48 Caveat 03 – Absolute value vs growth rate
06:17 Caveat 04 – Exact value vs average
07:05 Caveat 05 – Median, mode, range
07:50 Caveat 06 – Decile, quantile, quartile
08:49 Caveat 07 – Simple vs cumulative
09:25 Caveat 08 – Terms & Definitions
09:49 Example 02
This is the ninth theory session of the problem-solving test course. We will list some of the most important data interpretation traps and caveats of a test and learn what to do about them.
Today we will kick off with the following example from an official PST.
As always you might want to pause to video now and try to solve the question on your own.
Which of the following statements is a valid conclusion based on the data presented in Exhibit 1?
We’ll look at exhibit one and see that it is data from a recent visitor survey in the gallery.
We know that there are two parts of the graph splitted visits by priority visit as percent of all respondents and notice that the total number of respondents is six thousand and then the split of visitors by source.
Here we get percent of those who visited the area primarily to see the gallery, so it’s not all 6000 people.
By looking at the data labels we noticed that one of the segments is called the gallery was my main reason for visiting the area.
So, this is exactly the base for the second graph.
We also know that this is a random survey taken over the last month.
Now we are ready to tackle different options and look for a valid conclusion.
Option A. 24 percent of visitors spend money on an overnight hotel stay because of the gallery’s presence.
We know that 60 percent of people chose the gallery as their main reason for visiting the area and then 40 percent of them stayed overnight in the area at the hotel so that the number of people who stayed at a hotel and obviously paid for it because they wanted to see the gallery is 60 percent times 40 percent equals 24 percent.
So, this is true, and in the real PST we would not consider other options. We would just circle A and move on. But here for the sake of learning let’s consider other options as well.
Option B. 40 percent of visitors did not spend any money because of the gallery’s presence.
Well this is unknown, because there is no information on spending in general.
We know that 40 percent of people, these people here, did not have a gallery as the main reason for visiting the area.
But that does not mean that they do not spend money because of gallery’s presence.
And also, we don’t know how many people of the other 60 percent actually spend money because of gallery’s presence. So, option B is unknown. Option C. 50 percent of visitors to the gallery came on day trips from outside the Riverside area.
Well we know about 50 percent from here but these 50 percent refers only to the 60 percent, those who had gallery as their main reason for visiting the area.
But we did not know the split for the remaining 40 percent.
We don’t know how many of them came on day trips from outside local area.
So, C is also unknown. Option D. 60 percent of visitors only came to the Riverside area to see the gallery.
We also don’t know that, because we know that 60 percent of visitors had gallery as their main reason for visiting the area, but main is not the same thing as the only reason for visiting the area.
So, D is unknown as well.
So, our answer is A. One of the critical skills of a young consultant is being attentive to details, despite stress and tight deadlines. McKinsey PST is a perfect tool for testing this skill, as the test is full of Slash-film wrong expressions and mathematical and logical traps.
Below we will discuss the eight most popular things to watch out for in a PST. One. Whole versus part of whole. Supposed the revenue for three months is three hundred dollars and the profit one year are hundred twenty dollars.
We may be tempted to extrapolate the revenue to one year to get one thousand two hundred dollars, then the profit margin will be 10 percent.
But this is wrong.
Unless we know the extrapolation is legitimate and they can know it’s only from the text; the one your revenue can be larger or smaller than 1200 dollars.
Hence the profit margin in this case would be unknown.
Similarly, when they’re given monthly subscription fee and they’re working on annual revenues we must multiply the fee by 12 and by the number of subscribers.
And if we know that the salaries of white collar employees account for 30 percent of costs we should not assume that the total labour costs it’s 30 percent.
There might be other costs in the labour bucket including other categories of employees. Two. Absolute value versus share. Company A has an 80 percent market share in country one and Company B has a 10 percent market share and country two. Whose revenue is larger?
The answer is we don’t know because we do not know how large the markets of country one country two are. For example, if the size of country one’s market is one billion dollars, and the size of country two’s market is ten billion dollars, the revenue of company B is greater than the revenue of company A, despite lower market share.
However, if the markets are of the same size, the conclusion would be the opposite.
Three. Absolute value versus growth rate. Market a is growing at 20 percent per annum, while market B is growing at 2 percent per annum. Which the markets will be bigger in ten years if the trends continue?
Again, this is unknown. It depends on the size of the markets.
Of course, market a will grow more than market B, but if market B is hundred times the size of a market A the growth starts to play a minor role. Four. Exact value versus share.
Recall one the first questions of Kosher Franks.
Is it true that the sales of sliced meats grew by no less than one-point two percent over the past five years?
Given the average growth rate was one-point two percent.
Their answer is again we don’t know. The growth rates may maybe both below and about one-point two percent and still ensure the same one point to average growth rate.
Here’s an example.
If the growth rates are as follows, the compound average growth rate over the five years would be roughly one-point two percent. Even though in some years the growth rate was above one point two and, in some years, it was below 1.0 Five.
Median, mode and range.
Here we need to know a few concepts from statistics.
A median is the middle of a sorted list. A mode is the most common value in a list, and the range is the difference between the largest and the smallest values in a list.
For example, take the following list.
The average here would be about 18.83.
The median will be two plus three over 2 equals 2.5.
The mode would be 2, and the range would be a hundred minus two equals ninety-eight. Six. Decile, quintile and quartile.
Decile. 10 percent of the elements of a sort of list.
Quintile is 20 percent of the elements of a sort of list. And quartile is 25 percent of elements of a sorted list.
Consider the following example.
This list has 10 deciles, each consisting of two elements.
It also has five quintiles.
Each consisting of four elements.
And also, four quartiles.
Each consisting of five elements.
The bottom decile is here, the bottom quintile is here and the bottom quartile is here. The top decile this is this one, the top quintile is this one and the top quartile is this one.
Seven. Simple versus cumulative. In a cumulative graph each next point corresponds to the sum of all previous points plus a new value.
For example, have three values 1 2 and 3.
As simple graph would depict them as 1 2 and 3; but the cumulative graph would show them as 1, 1 plus 2, 3 and 3 plus 3, 6. Make sure you notice the word cumulative community in the title of the exhibit and you not confuse it with the simple graph.
8. Terms and definitions.
The test will introduce a lot of weird terms. Always check the text and look for definitions.
They will be there.
Also remember that profit per dollar of sales or profit per dollar of revenue means profit margin not profit in absolute value.
A perfect example full of little traps is these official PST question. You might want to pause the video at this point and try to solve the question on your own.
Which of the following cannot be concluded from the information presented in Exhibit 3, regarding the sample of customers analysed. We look at Exhibit 3 and notice the following: average one-year value in dollars, averaged 90 days number of transactions and average 90 days total revenue. We also notice that customers are split into five quintiles and we know that quintile is just 20 percent.
In the text we learned that there are 500000 Marcadia customers in the last year.
The customers are sorted according to the one-year customer value from lowest to highest. In one-year customer volume is defined as the profit made by Marcadia on purchases made by a customer in their first year since signing up. Now we are ready to consider all the options. Option A. Purchasing by customers in the first 90 days is an indicator of the value to Marcadia in their first year.
So, A essentially means: value in one year is proportional to purchasing within 90 days.
We’ll look at the exhibit and see that this is true.
The higher one-year value, the higher number of transactions and the higher total revenue.
So, A is true. Purchasing by customers in their first 90 days is indeed an indicator of their value in their first year.
So, A is true. And remember that we’re looking for falls or unknown. Option B. Quintile one of our customers with the lowest profit margin for Marcadia. Well B is actually unknown because we do not know the profit margin. And we do not know the profit margin because the one year of value or actually the profit for one year cannot be compared to total revenue for 90 days.
And we cannot extrapolate that all the revenue for 90 days to one year to search for the profit margin for one year.
So, B is unknown and B would be our answer in an actual test.
And at this point we would stop solving this question.
Mark B as the answer and move on. But for the purposes of learning let’s consider C and D as well. The average customer makes between two and three transactions in the first 90 days since signing up.
This is quite easy to check right?
We just take the average of these numbers: one point one, one point three, one point five, two points six, five points seven.
Then we can add up these numbers.
Once we take the average we see that it is bigger than two but smaller than 3.
So, C is true. And D the average One-Year customer value is 7.90.
Okay we just need to take the simple average of these numbers here because the quintiles are of the same size.
We find that their sum is thirty-nine points five.
And then the average is thirty-nine points five over five which is exactly seven points nine.
So, D is also true and B is our answer. The 8 caveats of the PST are: whole versus part; absolute versus share; absolute versus growth rate; exact versus average; median mode and range; decile, quantile and quartile; simple versus cumulative, and terms and definitions.
This is by no means an exhaustive list and you can expect other traps too, but if you learn not to make mistakes in these eight you’re well equipped for the test. And make sure you’re attentive to details.
That’s all for today.
Please leave your questions and observations in the comments below.
I will be happy to discuss thanks for your time and until next time.