#15 - Global, Justify

[Jon Denning]

Complete Question Explanation

The correct answer choice is (C).

Answer choice (A):

Answer choice (B):

Answer choice (C): This is the correct answer choice.

Answer choice (D):

Answer choice (E):


This explanation is still in progress. Please post any questions below!

[itsmathuri]

Hi there,

What would be the best process of attacking questions like this? I tend to have a bit of trouble with figuring out which element determines the whole game and end up testing multiple variables out which eats up time.

Thanks!

[Robert Carroll]

mathuri,

I diagrammed the game out again right now just to see how I would look at it if I had my diagram and didn't know what the answer was. My thought process when I saw this was a Justify question was...whose absence is powerful? My first thought was L - L is the only random in the game, and adding information about a random is often helpful in a Justify question generally. However, L is not in any answer! I'm not even sure L would have worked - I didn't pursue it further when I saw that no answer had L.

My next thought was that the F/H requirement for treasurer is pretty powerful. But we're trying to leave someone out for this question. So who, if left out, would lead to further consequences? I thought that H was a good place to look. If H is out, F is in, as treasurer, and G is out entirely (first rule). So now we have H and G out, so everyone else is in. K must be mayor, if in, and the remaining two people are councillor.

So, I did brute-force one answer...but it was the correct answer. How did I know to start there? Because it looked like leaving one of the options for treasurer out was going to have some consequences, and specifically, H being out still leaves F in, which is a restrictive variable - F's presence means G's absence.

If, in a Justify question, I brute-force 1 or 2, sometimes even 3, answers to get the right one, I don't think that's a big deal. I don't want to routinely diagram a lot of answers, so I need to select answers that are more "promising" because they give appropriate restriction.

Robert Carroll

[hope]

But couldn't A be correct as well?
Rule 1
F not G
G not F
However, both F and G can be out, right? If that is right then A could work. With Frost out, we could have...

M: K
T: H
C: L and J

OUT: F and G

Please let me know if I have the correct understanding of Rule 1 when the negative falls on the Necessary condition with both the rule and its contrapositive.

Thanks.

[Robert Carroll]

hope,

While we could have F and G both out, we don't need to. The selection of nominees and each office won't be completely determined if we have some situations with G in and some situations with G out. In your solution, because L is a random, we could just replace L by G, and now there's another solution that works. So putting F out does not completely determine things, because multiple solutions still work.

Your understanding of the first rule and its contrapositive was perfect:

F G

G F

Robert Carroll

[g_lawyered]

Hi P.S.,
After reading all the explanations posted, I see how answer choice C is correct. However, I don't understand why E can't be the correct answer? I chose it as answer because of my diagram. See below:

IN: F with t, J with m, H with c, and L with c

OUT: K and G.

Can someone direct what makes answer choice E incorrect here?
Thanks in advance!

[Robert Carroll]

GGIBA003,

Is there any other assignment of candidates that works and also has K out? If so, then answer choice (E) is not correct.

Can you explain why in your diagram all of those choices had to be made?

Robert Carroll

[g_lawyered]

Hi Robert,
I made the choice to test out answer choice E to see if K was the variable that "completed" the diagram as the question states. After reviewing, the explanation of Answer choice C I see that K can be out but I missed that throughout my PT. Here's how I diagrammed E out:
1. K being out means that J, G, or L can be with M. In this case, I chose H to be in c (rule 2 is in action) which makes J in m.
2. Since H is in m, F must be the one that goes in t. (rule 3)
3. Since F is in, G must be out (rule 1). Which leads to L has to be in c
This has both K and G out.

Because this is a MUST be True question, I know that the answer has to be correct in both/all diagrams. I also tested E by diagramming:
IN: H with t, J with c , G/L with m, and L/G with m

OUT: K and F.

Here's how I diagrammed diagram 2 for Answer choice E out:
1. K being out means that J, G, or L can be with M. In this case, I chose H to be with t. (rule 3).
2. Because I already had J with m in the 1st diagram. I wanted to test what other variable it could be with. But for my understanding, I didn't want to make a Mistaken Reversal of Rule 2. That because H isn't with C, J could be with m (J could be in m without H being in c. Did I understand that rule right?
So I diagrammed that either G/L could be with m

3. Since G is in, F must be out (rule 1). Either L/G could be with c.
This has both K and F out.

After observing both diagrams, I concluded that K can be out and it would determine which variables are in and that's why I chose answer E. Is Answer choice E incorrect because in diagram 2 it leaves open the possibility the L and G could be with either m or c. i didn't see this with the 1st diagram I drew out but somewhat see it with this diagram. Are my diagrams correct? Am I on the right track here?

Thanks in advance!

[Adam Tyson]

E is incorrect because there ARE at least two diagrams for what happens when K is out! The whole point of this kind of question about a complete determination of the selection and placement of the variables is that the correct answer will guarantee one and only one solution to the game. You should know exactly who is in AND exactly what offices they hold. The fact that you had to choose something to be in means that it wasn't forced in, and right away you should stop diagramming and cross that answer out.

I started as Robert did, with H, because I saw that H out would force F to be Treasurer, and that's powerful because I not only know something that has to be in, but I know which spot it goes in. All the rest flowed from there, as he explained.

But if I had been tempted by answer E, here's what that process would have looked like:

K is out. What does that tell me? Well, F and G don't get along, so one of them is also out and the other one must be in because there isn't room in the out group for both of them. Not sure yet which one is which, but I know for sure that the other variables - H, J, and L - must be in. Do I know where any of them go? No, I don't. H might be Treasurer, but then again F still could be. J might be Mayor, but might not.

Stop. This answer is dead to me. It's not forcing me to choose between F and G, and it isn't forcing me to put any one variable in any one space. Don't think about what COULD happen, because this question is all about what MUST happen. Any more work on it is a waste of time!

[g_lawyered]

Hi Adam,
Your diagram really clarified that up. I now see why E is not a MUST be true answer choice. Thank you so much!