McKinsey PST 04: Conclusion

This is the fourth theory session of the Problem Solving Test Course. I introduce conclusion questions, explain the difference among true, false, and unknown, and demonstrate it on a few examples.

[TRANSCRIPT]

This is the fourth theory session of the problem-solving test course, devoted to conclusion questions. I will explain what is so special about conclusion questions and where mistakes may be hiding.
After that we’ll discuss a solution algorithm which will help us tackle conclusion questions and then we’ll apply to several examples.

Recall that there are four major question types: premise. fact, conclusion and the last 13 percent, or everything else.
Today we’re talking about the third type: conclusion. Conclusion questions have only two subtypes: those requiring computation and those not requiring computation.

Recall the differences among question types.
A premise doesn’t have to be true or based on the data in the text or exhibits, it might be a completely new piece of information.
However, if we assume it’s truth, it allows us to make certain conclusions about a fact stated in the text.
In comparison a fact is true based on the data you just interpreted it.
And the conclusion has to follow from the data, but some options might not follow from the data, be false or unknown.
We’ll talk about it in a moment.
Let us look at an example of a conclusion question not requiring calculations. Based on the information in Table 1: which of the following is a valid conclusion? Options are very similar.
We just need to conclude in each of the four weeks all four executives of
El Goog worked less than 40 hours.
Let us test the options one by one. In week one CEO worked thirty-nine hours, CFO worked thirty-eight hours, CTO thirty hours and COO thirty-nine hours. All less than 40 hours.

So, Option A is a valid conclusion. In a real test, we would not read further, but would mark A as the answer and move on.
But here for the sake of learning, let us look at other options. In week two all but COO all worked less than 40 hours but COO rocked more than 40 hours.
So, we cannot conclude that in a week to all executives worked less than 40 hours, so B is false. In week 3 all but COO worked less than 40 hours, but we do not know how many hours they COO worked.
If he worked 40 hours or more the option would be false. If he worked less than 40 hours, the option would be true. In this uncertainty, all we can say is that we do not know if C is true or false. Mark it unknown. In week four the situation changes.
We still know that CEO and CFO worked less than 40 hours and we do not know how many hours CEO worked. But we do know that CTO worked more than 40 hours. That means that option D is false regardless of CEO works hours a week four, because we already know that not all executives worked less than 40 hours.
What have we learned from this example?
We have learned that a statement is true if all its sub statements are true.
A statement is false, if at least one of its sub statements is false.
And the statement is unknown, if at least one of its sub statements is unknown and there are no false sub statements. This rule will be important for testing options.
The algorithm we will use for solving conclusion questions has three steps: understand the question, drill down options one by one and make a fact-based decision.
The first step is to understand the question.
The conclusion question is usually much simpler than premise or fact.
All we need to understand is: whether we are looking for a true, a false or an unknown statement, or maybe for a combination thereof as in the case of not a valid conclusion. Pay attention to false and not: about 20 percent of mistakes in conclusion questions come from forgetting about them and circling a true option.
You will probably make this mistake in the practice part of the course too, which is good. This way you will learn the trick better.
The second step is to examine each option separately. In these questions type we do not need to read all options and this can save us time.
However, if we do read an option we need to read it extremely carefully, paying attention to all the details, such as: subjects, their actions, numbers, place, time and inclusion exclusion words. If we understand that an option is very difficult or time consuming. We should put it on hold and look for easy ones.
Chances are that the correct option will be easier to check and we will quickly pick it up. All that we will eliminate all other options and discover that the difficult one has to be the right answer. To do a quick check, try to visualize your problem solving and draw answer options and exhibits.
This technique helps speed up the process.
The third step is to make a fact-based conclusion. Actually, steps two and three are done simultaneously.
Here it is important to note that all our conclusions must be based on specific calculations and data points in the text and exhibits. They should never be based on your professional experience, common sense or gut feeling.
So, let’s make sure we know what we base our conclusion on.
The difference between true false and unknown is something we already know. And option is true, if all required supporting facts are true.
And option is false, if at least one required supporting facts is false.
An option is unknown, if at least one required supporting fact is unknown and there are no known false facts.

One important point here.
Once we have found the right answer we should not read other options just to confirm it’s a waste of time.
Let us better invest time into studying our candid option deeper and more carefully. Now we will put the ideas of the session into practice.

Look at this official PST question.
Okay so let’s follow our algorithm step by step and consider all the options.
The question says: what you can conclude from the information regarding the rent estate market given in an exhibit Sour? so we’re looking for a true conclusion here. And we need to examine exhibit four.
We look at exhibit 4 and see no title here.
That means we need to go back to the text and figure out what the exhibit is about.
Okay. Four age groups. It’s clear. Here there are. Current and forecasted number of households in thousands. Exhibit four includes households who have respective minimum income to for antistate trends?
Okay so this is important, so that means that that’s not the total market or overall population, it’s just those who can afford the rent.
The percentage on the right side of the exhibit shows the percentage growth of the segment over the next 10 years.
Now we can drill options one by one and check if they are true.
A. There are at least 10 percent fewer 65 plus households than 50 65 households.
Let’s check that. 10 percent of 986 is about 99. Right.
If the difference was at least 10 percent then the number of 65 plus households would be eight eighty-seven.
But 887 is less than 899.
So that means that the difference between 50 65 and 65 plus households is less than 10 percent not more than 10 percent.
So, A is actually false. B. 35 to 49 segment will experience the lowest growth rate in the next 10 years.
So, this is our segment currently and this is our segment in ten years.

We don’t know this segment here but we know that it is growing at 5 percent. Our segment here is growing, at well, I guess it’s less than 5 percent, right?
Because 5 percent would be 57 and a half and the difference here is less than 50.
So, the growth is less in fact percent. And if you look at other segments for example 50 to 65, this growth is definitely more than 10 percent and this growth here is also more than 10 percent.
So that means that the 35 to 49 segments will indeed experience the lowest growth rate in the next 10 years.
So, this is true, but we were looking for the true option and B is through.
So, B is our answer.
And we do not need to read C or D.
We just mark B as our answer and move on.
Let’s synthesize what we have learned today. A valid conclusion must follow from the fact; however, conclusions might also be false and unknown.
We solved conclusion questions via three steps. One: understand the question.
Do we need true statements or false statements or not valid conclusions.
Two: drill down options one by one, review keywords and tackle easy options.
Three: make a fact-based conclusion.
Be sure to be fact based and skip unnecessary options.
That’s all for today.