1. What is it?

When you get into consulting, you will hear the term “fact-basedprobably a million times each day. Consulting is the business of making conclusions based on facts. We make many different types of conclusions throughout the course of any project: from top-level to granular level, from functions to functions, from industries to industries, etc. It is such an important aspect of consulting that McKinsey puts a decent amount of  weight on it in the Problem Solving Test.

I personally think this is the most difficult, interesting, and crucial question type in the test. If I were to write an analytical entrance test for my own firm, the weight of this question type would be even higher than the McKinsey Problem Solving Test.

So let’s get into it: Fact-based conclusion questions are those testing your ability to draw and recognize sound and logical conclusions based on a set of data/ facts provided.

management consulting prep pst fact based conclusion 3

Examples of question format

  • Which of the following statements is a valid conclusion based on …?
  • Which of the following statements can be concluded from …?

Difference between fact-based conclusions and reading facts

In some aspects, fact-based conclusions and reading facts questions are similar. In both cases, you are given a set of facts/ data and are asked to read vs draw a conclusion from it.

The key difference is that reading facts questions only test your ability to read the facts and do minor calculations while fact-based conclusion questions require you to touch on more sophisticated logic and reasoning skills. Of course there is no clear cut definition on what is considered “minor calculations” and what is considered “sophisticated logic and reasoning”.

The two extreme ends need two different sets of skills and techniques – there will also be questions that require both. So it is not as important to distinguish the two types as it is to know and master the skills needed for both types.

Difference between fact-based conclusions and root-cause reasons

Unlike the case right above, distinguishing fact-based conclusions and root-cause reasons is much more important. There is a clear cut line when a question asks you to give a potential reason / hypothesis for a set of facts/ data (root-cause reasons) or a conclusion-drawn from the facts/ data (fact-based conclusion).

management consulting prep pst root cause

2. Conclusive logic 101 – TRUE/ FALSE/ UNPROVEN conclusions

Any proposed conclusion must fall into one of the following three groups. It is either (1) proven TRUE, (2) proven FALSE, or (3) unproven. The key to answer fact-based conclusions is to identify which of the above three groups a proposed conclusion belongs to.

Theoretical illustration

A is an entity that has n parts. X is a quality.

1 – Proven TRUE conclusion:
“A is X” when and only when ALL A1, A2, A3, … An is X.

2 – Proven FALSE conclusion:
“A is X” when ANY of A1, A2, A3, … An is NOT X.

3 – Unproven conclusion:
“A is X” when ( NOT YET ALL A1, A2, A3, … An is X ) and (NONE of A1, A2, A3, … An is NOT X)

Real life illustration

Let’s look at a conclusion: “The Boston Celtics (a professional basketball team) were undefeated in December.”

It is Proven TRUE when: All games of the Boston Celtics in December have been played and they didn’t lose a game

It is Proven FALSE when: You can point out any game the Boston Celtics lost in December

It is Un-proven when: You have not looked at all games the team played in December

3. Conclusive logic 102 – fit-well vs fact-based conclusions

As discussed above, a proposed conclusion can be in one of the three groups. However, the most confusing and easily misleading is the unproven group. Many times, the question will propose a conclusion that fits really well with all the facts/ data provided. However, if that conclusion can not be supported by the facts/ data, it can not be a proven true conclusion. Let’s look at a simple example:

* * *

Fact A: The campus looks so empty now.

Conclusion C1: It’s Christmas eve!

Conclusion C2: Students of this university are just not interested in studying!

Conclusion C3: There are less professors around today!

All of the above conclusions fit well with Fact A.

  • C1 “fits” well because if it’s Christmas eve, students will be at home celebrating Christmas with their family. That makes the campus look empty.
  • C2 “fits” well because if this school’s students don’t like studying, they will probably skip classes. That makes also the campus looks empty.
  • C3 “fits” well because if professors are not around, there will probably be less classes today.

But none of the above can be concluded. I will deny those conclusions by pointing out scenarios where Fact A still holds and conclusions C1, C2, C3 are false.

  • C1 can not be concluded because what if it’s right in the middle of September, the campus is empty just because it’s Sunday?
  • C2 can not be concluded because what if this is Harvard campus; it is empty just because there’s a hurricane in the area and students are encouraged to stay at home?
  • C3 cannot be concluded because what if in fact it’s a professors conference day, all classes are canceled but all professors have to attend?

Now here is one good and sound conclusion: “You would meet fewer students  if you took a campus tour right now” . If the campus looks empty right now,  you will surely meet less people on campus. This conclusion is supported by fact A!

Too much theory? It’s finally time for a very McKinsey PST-like question example!

4. Fact-based conclusion question – Bingham Mine

This question is written based on an official McKinsey practice PST question.

* * *

The McKinsey team has an interview with the Chief Operation of the New Bingham Mine, Salt Lake City. During the interview, the following facts have been gathered:

  • The factory must have at least one safety inspector 24 hours a day, seven days a week, to satisfy Federal and State labor regulations.
  • To maximize operational efficiency, there must be exactly 10 line workers operating the mine.
  • The mine operates from 8am until 5pm Monday to Sunday.
  • The mine employs 4 safety inspectors and 16 line workers to make 20 direct workers in total.
  • Total weekly employee cost for the Bingham Mine is $16,000.

Which of the following statements is a valid conclusion?

A. One fifth of the total direct workers cost for the mine is for safety inspectors
B. At least one safety inspector must work more than 40 hours per week
C. Line workers do not work more than 40 hours per week
D. The majority of the mine’s employee cost is for line workers

Click to see answer keys

A – Fit-well but non Fact-based
There are 4 inspectors out of 20 direct workers so it seems like cost of inspector can very well be 1 / 5 of total direct worker cost. But a missing piece of data to conclude that is: does each person get a similar total income?

C – Fit-well but non fact-based
The mine opens for 9 hours per day, 7 days per week, and there must be 10 line workers at a time, so it is 630 man hours per week at the line positions. There are 16 line workers, so on average each must work only 39 hours per week. This seems to fit very well with the proposed conclusion: line workers do not work more than 40 hours per week. However, a missing piece of data to conclude that is: does every line worker works for the same amount of time (if not, there can be some who work over 40 hours while others work less)?

D – Fit-well but non fact-based
Similar to A, there are more line workers, so it seems like the total cost for line workers is more than the total cost for safety inspectors. But a missing piece of data needed to conclude that is: is the cost of each worker similar?

Only B is a proven true conclusion based on the provided facts. There are 24 x 7 = 168 inspector hours needed in a week, equaling 42 hours per week per inspector. So there must be one who works more than 40 hours.

5. Twist type 1: False conclusions

Identifying proven true conclusions is an important foundation to master all conclusion-related questions. However, most conclusion-related questions in the McKinsey Problem Solving Test will be given in other formats. Here in this section we will discover and learn about the two types of twists: (1) False conclusions and (2) Conclusions reversed. Let’s start with the first one.

* * *

As discussed above, any proposed conclusions must fall into one of the following three groups: Proven TRUE, Proven FALSE, and Unproven. This twist is when a question asks you to identify the FALSE conclusion instead of the TRUE conclusion.

Typical question format

Which of the following statements is FALSE based on … ?

Methodology

A proposed conclusion is proven false when you can point out at least one instance where the conclusion is wrong. Similarly, with true conclusion questions, unproven conclusions should also not be selected.

Notice that proven FALSE conclusions are NOT conclusions not proven TRUE. A conclusion will stay unproven until it is proved to be TRUE or FALSE.

Example

This question is written based on an official McKinsey practice PST question.

* * *

Table 1 

Which of the following statements is FALSE based on Table 1?

A. Rancho Engineering had lower average economic growth in the last five years than Silencer, Inc.
B. Rancho Engineering had higher average economic growth in the last five years than Silencer, Inc.
C. Investment risk rating is based on the difference between maximum and minimum revenue growth in the past five years.
D. Potential rating is based on the maximum recent revenue.

Click to see answer keys

Of A and B, A seems to be false and B seems to be true. However, both of them are unproven. The maximum and minimum figures are not enough to conclude the average.

We don’t know if C is right or not, but we know that it is not proven false. Of the provided data, there is no instance where the larger difference between maximum and minimum recent revenue growth indicate smaller risk (and vice versa).

With D, we know for sure that it is proven false because we can point out an instance where the assertion conflicts with the data (Farhan Discovery vs Silencer, Inc.).

6.Twist type 2: Conclusions reversed

Very often, conclusion questions in the McKinsey Problem Solving Test is given in the Reversed format. They give you the conclusion first and let you pick what facts/ data would be enough to come up with the stated conclusion.

The key to answering this type of question is being able to recognize which proposed fact makes the stated conclusion proven or unproven.

Let’s try an example: 

This question is written based on an official McKinsey practice PST question

* * *

FOCUS Travel is a premium Russian tourism company, offering tours to South East Asian countries. Facing the economic downturn, FOCUS revenue has been hurt badly. While the CFO (Chief Finance Officer) proposed an overall price cut to stay competitive, the CMO (Chief Marketing Officer) is concerned that a price reduction would negatively impact the premium perceptions of the brand, which drives a lot of sales.

Which of the following statements, if TRUE, would best support the CMO’s assertion?

A. In a recent survey, FOCUS’s customers quoted “price” as the most important indicator in choosing travel agencies in a list of ten factors
B. In a recent survey, FOCUS’s customers quoted “price” as the most important indicator of quality in a list of ten factors
C. In a recent survey, there were customers who said they would not buy FOCUS’s services if there was a 10% price increase
D. In a recent survey, there were customers who said they would not buy FOCUS’s services if there was a 10% price decrease

* * *

Click to see answer keys


Solve it together
In this question, the “conclusion” has been given to us: Price reduction will negatively impact the premium perception, which will in turn negatively impact sales.

Of the four proposed answers, which facts are enough to prove the provided “conclusion” above?
A: This fact is only enough to conclude that price will impact sales. Not enough to prove that price reduction will negatively impact sales.
C: This fact is irrelevant.
D: This fact is not enough to conclude that price reduction will negatively impact sales because not all customers say so.The word “there were” can be understood as either a minority or a majority. It is only enough to conclude the proposed conclusions when “there were” is replaced with “the majority of” or “all“.

With B, we can logically infer that price reduction will negatively impact the quality perception, which in turn will lead to sales being hurt.

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