# McKinsey Problem Solving Test Fact-based Conclusion Question

## 1. What is it?

Once you get into consulting, you will probably hear the term “fact-based” a million times a day. Consulting is the business of making conclusions based on facts. We face tons of different problems throughout the course of any project: from the top to the granular level, from function to function, from industry to industry, etc. Fact-based conclusion is such a fundamental aspect of consulting that it weighs in heavily on the Problem Solving Test.

Fact-based conclusion questions test your ability to draw and recognize sound and logical conclusions based on a set of data/facts provided.

Examples of question format

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

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 and then 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 dealing with sophisticated logic and reasoning skills.

Of course, it’s necessary to keep in mind that there is no definite line between “minor calculations” or “sophisticated logic and reasoning”. Nevertheless, two extreme ends need two different sets of skills and techniques, although there will also be questions that require both. All in all, it is not as important to distinguish between the two types as it is to know and master the skills needed for both.

Sometimes even though the word “conclude” is used, questions don’t require any logical reasoning, just your ability to read facts and perform basic calculations. In these cases, I still classify these questions into the reading-facts category.

Fact-Based Conclusion vs. Root-Cause Reasons

Unlike the case right above, distinguishing fact-based conclusion and root-cause reason is much more important. There is a clear difference between determining a potential reason or hypothesis for a set of facts/data (root-cause reasons) and drawing a conclusion from those facts/data (fact-based conclusion).

Root-cause Reason Fact-based Conclusion
Give you a set of facts A
Give you a set of facts A
Ask you to identify 1 or more potential reasons B so that if B is true, A is true
Ask you to draw a conclusion C so that if A is true, C is true
If fact A is true, B is NOT necessarily true
If fact A is true, C is TRUE

## 2. LOGIC LESSON 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 answering fact-based conclusion questions is to identify which of the three groups above 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 the games of the Boston Celtics in December have been played and they didn’t lose any game.

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

It is UNPROVEN when: You have not looked at all the games the team played in December.

## 3. LOGIC LESSON 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 misleading is the unproven group. Often times, the question will propose a conclusion that seems to fit really well with the case. However, if the facts/data available are not enough to support that conclusion, it cannot 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 fewer professors around today!

All of the above conclusions fit well with Fact A.

• C1 fits because if it’s Christmas Eve, students will be at home celebrating Christmas with their family. That would explain why the campus looks empty.
• C2 fits because if this school’s students don’t like studying, they will probably skip classes. That would explain why the campus looks empty.
• C3 fits well because if the professors are not around, there will probably be fewer classes today.

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

• C1 cannot be concluded because it might be in the middle of September, or the campus might be empty because it’s Sunday
• C2 cannot be concluded because the campus might be empty just because there’s a hurricane in the area and students are encouraged to stay at home
• C3 cannot be concluded because it might be staff conference day, which means all classes are canceled but the professors will still have to be present

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

## 4. Example - Fact-based conclusion question – Bingham Mine

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

The McKinsey team has an interview with the Chief Operating Officer 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, in accordance with 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 workers in total.
• The total weekly labor cost for the Bingham Mine is \$16,000.

Which of the following statements is a valid conclusion?

A. One fifth of the total labor 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 labor cost is for line workers

A – Fit-well but not fact-based

There are 4 inspectors out of 20 employees so it seems like cost of inspector can very well be 1 / 5 of total labor cost. But a missing piece of data to conclude that is: does each person get a similar total income?

C – Fit well but not 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 of them only needs to work 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 the same amount of time (if not, there can be some who work over 40 hours while others work less)?

D – Fit well but not 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: does each worker get paid the same amount?

Only B is proven true by the provided facts. There are 24 * 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.

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. In this section, we will learn about the two types of twists: (1) False conclusions and (2) Conclusions reversed. Let’s start with the first one.

## 5. Twist type 1: False conclusions

As discussed above, any proposed conclusion must fall into one of the following three groups: Proven TRUEProven 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 …?
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.

Data on Investment Assessments for Four Subsidiaries Under Consideration

Measure Explanation Rancho Engineering Farhan Discovery Raju Foundation Silencer, Inc.
Maximum recent revenue growth
Highest one year revenue growth in the last 5 years
15%
6%
12%
10%
Minimum recent revenue growth
Lowest one year economic growth in the last 5 years
6%
5%
1%
2%
Investment risk rating
Ranked A: highest risk to E: lowest risk
B
D
A
B
Potential rating
Ranked 1: least potential to 10: most potential
7
6
7
5

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.

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. In 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 are given in a reversed format. You will be given the conclusion first and asked to pick what facts/ data would be enough to come up with that conclusion.

The key to answering this type of question is 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.

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 perception 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

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 hurt to sales.