McKinsey PST C - Detailed answers

McKinsey PST C  is a great test to take at the beginning of your PST preparation (as well as McKinsey PST A, and McKinsey PST B). These tests will be really helpful to give you a sense of what to expect in the problem solving test. 

However, the answers provided by McKinsey in these documents are sometimes not very detailed. As a consequence, we have regularly had candidates reaching out to us and asking for help to understand some of the official answers provided by McKinsey since we launched IGotAnOffer. 

We already published detailed answers for the McKinsey PST A and detailed answers for the McKinsey PST B at the beginning of this year. So let's cover the third test that's made available by McKinsey today: McKinsey PST C. So far candidates have asked us to write detailed answers for the following questions in McKinsey PST C:

If there are any additional questions you would like us to write a detailed answer for, leave a comment at the bottom of this page and our team will get back to you.

In our experience successful candidates really go in-depth to understand their mistakes when preparing for the McKinsey problem solving test. In addition, they also study the answers to questions which they answered CORRECTLY and try to look for ways to answer the question FASTER. This is why the three tests in our McKinsey PST Training Programme contain detailed answers with tips to answer questions as fast as possible. 

Right, let's now step through each question one by one. If you have not already downloaded McKinsey PST C, you can find it here.

McKinsey PST C - Question 11 
Candidate question

I am having difficulties with question 11 from McKinsey PST C. The answer says 'high level of sickness ... may make productivity lower'. I do not understand this. Is there any chance you could help? Thank you.

By the way, thanks for your McKinsey PST tests. The answers are much more detailed than in the official PST which is very helpful.

IGotAnOffer answer 

If a lot of staff fall sick, then they will still get paid but fewer items will be handled, so the proposed measure would suggest that productivity has fallen. However, what we want to measure with productivity is how many items an employee can process under normal conditions. In this case productivity is low under normal conditions, and we are trying to think about what processes could be changed to increase it.

However, there is nothing the company can do about staff falling sick, so the proposed measure would not be very relevant. This is just an example however, and there are other reasons as suggested in the answer key why this measure would not be very relevant. Training would have the same effect, where staff is taking time away from processing items but still getting paid.

McKinsey PST C - Question 12 
Candidate question

I understand that answer C is the good one, however it is a bit hard to read the % from the graphs to be honest. In addition, I am not sure why B is false? Could you help me understand that?

IGotAnOffer answer

We agree that graphs aren't always easy to read. One thing you could do to make it easier is to draw additional lines at the mid-point between existing ones to get a better idea of the number the graph is showing.

Why did you think question B was correct? Answer B suggests that the number of hours worked at that time were sufficient to cover the number of items received. However, you have no information about how many hours are required to handle items in this period, nor about how many hours were worked in week -3, or how many items were handled. All the data you have is expressed in percentages of the first week's number so the only thing you could evaluate are changes from one weekly period to another. This is why answer B is incorrect.

For answer C, the relevant changes would be percentage changes since the numbers are given as an index, a value relative to the starting value in week -3. So the idea would be to see if the relative increase in hours worked is enough to cover the relative increase in items arriving. But in fact, you do not even need to calculate the percentages, since hours worked decreased while items arriving increased! So clearly there wasn't a sufficiently large increase in hours worked to cover the higher amount of items arriving, since hours were actually lower.

However, we understand how the question can be confusing because it asks about whether the change is proportional. In this context, proportional means in the same direction, as otherwise the option would have asked if the two variables are "inversely proportional".

McKinsey PST C - Question 15 
Candidate question

I was wondering if you could please help me understand question 15 from McK test C?

Answer C states that there 'are differing levels in the average volume of trash per customer in the different cities.' The answer indicates that Answer C does NOT help explain the differences in net profit margins.

Whilst I do agree that the fees are set per month, in the introduction it says that 'The monthly fee depends on the volume of trash to be handled.' That gives me an indication that although a monthly fee, the fee is very much dependent on the volume of trash (i.e., for instance, the price is set every beginning of month, depending how much trash was disposed of last month).

IGotAnOffer answer

You are right that the fees depend on the volume of trash collected, as mentioned in the introduction. But this is exactly why the volume should not affect the profit margin. Indeed, if the differences in volume are already reflected in the revenues and cost, then they cannot explain any differences in profit margin in the cities.

Suppose that there is 10% more trash to be collected in Milwaukee than in San Diego, then the cost of collecting the extra garbage will be 10% higher in Milwaukee than in San Diego. In fact you are told that the fee "covers the cost of handling the waste on the landfill site where it is deposited." But the fee should be 10% higher since the fee is based on the volume. So overall the margin would be the same in both cities if volume was the only difference.

McKinsey PST C - Question 16 
Candidate question

Thanks for the McKinsey PST Training Programme, I have already started to improve. I have another question about McKinsey PST C, Q16?

The answer key does not explain in details the formula for this calculation. Can you elaborate on the precise formula please? Is there any shortcut to get the right answer? It seems like a lot of calculations! I’m wondering if this is the type of question I should skip.

IGotAnOffer answer

The formula you are looking for should give you the number of customers at which the profit is zero. Then you can pick the answer that gives a number of customers greater or equal than your result.

Let's start with the formula for profit:

Profit = revenue - cost = (number of customers x fee per customer) - (weekly fixed costs + weekly variable costs)

The fee per customer is $100, the weekly fixed costs are equal to five times $2,000 (the daily fixed costs multiplied by the number of times the crew operates per week), which is $10,000 and the weekly variable cost is the cost of disposing of the garbage at the landfill. This is given by $15 x total number of tons per week. The number of tons of garbage per week is then given by average weight of garbage per customer per week times the number of customers so it is equal to 2 x 0.1 x number of customers.

Therefore you can rewrite the formula for profit as:

Profit = (number of customers x 100) - (10,000 + 15 x 0.2 x number of customers) = (number of customers) x (100 - 15 x 0.2) - 10,000

Set this equal to zero and re-arrange to get: number of customer to break even = 10,000 / 97 = 103. So C is the correct answer.

Yes this is a fairly long question, though setting up the equation as I did above should take less than 2 minutes as it is a standard profit equation. What takes longer is calculating 10,000 / 97.

However, you can start by eliminating answers, since clearly 10,000 / 97 is greater than 10,000 / 100 which is 100, so A and B cannot be right. Then to choose between C and D it might be quicker to verify each answer by multiplication rather than do the division: 97 x 108 is equal to (100-3) x 108 which is 100 x 108 - 3 x 108 which is 10,800 - 324 which you can see is not equal to 10,000 (or if you start from 104, you quickly get the correct answer).

McKinsey PST C - Question 18 
Candidate question

Can you explain why C cannot be the right answer?

IGotAnOffer answer

We agree that the conclusion is not very clear on this one. Our feeling is that, if anything, option C would explain why the proportion of large businesses that are aware of the service is larger than the proportion of small businesses. But it does not in itself explain why there are fewer large businesses that are current customers of the company.

McKinsey PST C - Question 21 
Candidate question

I understand that B is the correct because $7000/ t 6800=1.02. But I am not sure where I should use the number of employees in this question?

IGotAnOffer answer

You are told that the "total weekly employee cost [...] is $7,000" just above the graph, and the question asks the "employee cost" per ton of waste, so you don't have to worry about how this total employee cost is calculated.

You should take the word "employee cost" in the question as meaning the same as "employee cost" in the description, i.e. "total weekly employee cost". What you need to keep in mind is that if the question would like you to do additional calculations, then it would ask for it specifically, for example by asking for employee cost per employee per ton of waste.

McKinsey PST C - Question 22 
Candidate question

I have doubt about Question 22 from Mckinsey official PST practice test C. The answer says the new premium income is around $825m which increased about 18% over the original premium income which is $140m?

IGotAnOffer answer

You are told in the text that the original premium income is $700m. You are then told in the question to assume that operations cost remain constant. Since in the current year operations cost represent 20% of premium income, then operations cost are 0.2 x 700 = $140m. So you should assume that in the following year operations cost is still $140m. In addition, you are told to assume that claims cost remain at 83% of premium income (the new premium income that you need to calculate).

To break even, we need that income = costs (so profits = 0). This means that we need Premium income = operations cost + claims cost. 

Let "M" represent premium income, then the equation you want to solve is: M = $140 + 0.83 x M.

Solving this gives you: M = 140 / 0.17 = 824.

Finally, since the question asks the growth rate needed to go from $700m to $824, you need to calculate: (824 -700) / 700 = 18%.

McKinsey PST C - Question 23 
Candidate question

I am unable to fully understand the explanation provided in McKinsey Practice Test C (2006) for the InCo Case, in particular, questions 23 and 25. Please could you explain in a better way?

IGotAnOffer answer

That question refers to the profit structure you are given in the previous description. This is an insurance company, so its main source of income is from premium. Premium is the monthly or annual fee that customers pay to be covered by their insurance.

On the other hand, the company incurs claim costs. This corresponds to the money the company has to pay out to customers who had an accident and claimed their insurance. Claim costs have a value corresponding to 83% of income.

Finally, the company also faces operations costs, probably corresponding to the cost of employees processing customer claims and other miscellaneous expenses, including administration costs. This accounts for 20% of income.

The question asks: which of these three aspects should the company focus on to increase profits.

Intuitively, increasing income would have the largest impact, since it is the largest amount of all four options. So 1% of income represents more than 1% of claim cost or more than 1% of operations or administration costs, and therefore a 1% increase in income would have more impact on profits than the other alternatives.

However, you are told that claim costs increase proportionally to the increase in premium income. Therefore, increasing premium income by 1% would not have the desired effect, since most of that increase would be counterbalanced by an increase in costs, and therefore would not translate in a significant increase in profit. As a result, the second best option, decreasing claims cost, would have the largest impact.

McKinsey PST C - Question 24 
Candidate question

I am not sure I understand Exhibit 1 correctly for this question. Can you explain what I need to check and what is the shortest way to get the right answer? Can I eliminate C and D as they are just inferring and I need precise info?

IGotAnOffer answer

Yes, you can eliminate C and D because they would require additional information to be verified. The graph shows you how much of total income is generated by different policies (i.e. different individual customers). The graph therefore charts cumulative income per customer.

In addition, the x-axis is ordered by descending premium (i.e. descending price of policies). The most expensive policies sold are to the left of the graph and the cheapest to the right of the graph. So the group A that is highlighted for that question represents the 33% cheapest policies sold, and they correspond to 2% of the company's income. Intuitively, many policies are sold for a low price, and even though they represent a decent portion of total policies (33%), their price is so low that they only account for 2% of the firm's income.

To check option A, all you need to do is calculate how much these customers cost on average, and how much they bring in income on average. Since group A corresponds to 33% of policies and there are a total of 350,000 policies sold, then group A corresponds to 117,000 policies sold. At $200 of average cost per policy, this would amount to $23.4m in cost for this group. The average income they bring corresponds to 2% of total income, which is $700m according to the graph, so they bring in $14m, which is clearly below their cost.

Notice that you could have been even quicker on this question by noting that all you are given is average costs, and not individual cost. So it is clearly not possible to conclude option B. And you can eliminate option C and D as mentioned above.

McKinsey PST C - Question 25 
Candidate question

I am unable to fully understand the explanation provided in McKinsey Practice Test C (2006) for the InCo Case, in particular, questions 23 and 25. Please could you explain in a better way?

IGotAnOffer answer

This question requires you to calculate the average premium income per broker in different classes (or pairs of classes). So first, you should calculate the premium income generated in each of the classes, and then divide the respective total premium income by the total number of brokers, depending on what the option asks:

In option A, you need to calculate the average income per broker of class B and the average income per broker of class C. This is given by:

Class B: (Total income of class B) / (Number of brokers in class B) = (0.49 x 670) / 300 = $1.1m per broker

Class C: (Total income of class C) / (Number of brokers in class C) = (0.25 x 670) / 100 = $1.7m per broker

So option A is incorrect since the average income of class B brokers is smaller than the average income of class C brokers.

In option B, by contrast, you get:

Class A and C: (Total income of class A and C) / (Number of brokers in class A and C) = ((0.26 + 0.25) x 670) / (600 + 100) = $0.5m per broker

Class B: (Total income of class B) / (Number of brokers in class B) = (0.49 x 670) / 300 = $1.1m per broker

So option B is incorrect since the average income of class B brokers is larger than the average income of class A and class C brokers.

The confusing part might be that the average of class A and C is not the same as the average of the average of A and the average of C. If you did this calculation, you should see that it would give you a different answer.

McKinsey PST C - Question 26 
Candidate question

I don’t understand how to reach the right answer. Can you explain please?

IGotAnOffer answer

For this type of question, you need to assume that all statements are true, and think whether or not they would be a good argument for stopping business with the underperforming brokers.

The primary reason for stopping business with underperforming brokers would obviously be that they are underperforming. But you are told in the box above that discontinuing relationships with the brokers might come at a cost, so you would need an additional reason.

The question is about which of the additional reasons is the strongest argument.

Option A is not an argument for discontinuing relationships as it is not directly related to the benefit of discontinuing these relationships.

Option B is also not directly related to the cost of discontinuing the relationship, although it might be relevant as you are told that these smaller broker matter less in terms of relationships lost.

Option C is also irrelevant, since it could be the case that these smaller policies are actually profitable.

Finally, option D provides the most relevant reason why these relationships should be discontinued, since it suggests that these underperforming brokers create an additional cost to the company, on top of providing poor performance.

Any questions?

If you would like us to answer any further questions about McKinsey PST C please don’t hesitate to ask them in the comment section below and our team will get back to you.

Additional resources

If you would like to learn a method to consistently crack the PST you can get started below. More than 80% of students who use our McKinsey PST Training Programme are successful.

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