#23 - Global, Rule Substitution

[Administrator]

Please post your questions below!

[Kellyg]

I'm still struggling with rule substitution even after watching the powerscore module. Should I simply plug in each answer and see the results? This always is too time consuming even when i cross out the initially wrong answers (those that introduce new rules)

[Malila Robinson]

Hi Kellyg,
I think you are asking a general question, rather than asking for the specifics of this question. If that is not the case please comment again and one of us will go through this question in more detail.
For rule substitution questions you want to look at the rule they want you to take out and see what direct effect it had on the game. Then you are looking for the answer choice that would cause that exact effect to happen to the game. And yes, this question appears to be a bit more time consuming, because you need to work through each answer choice to see if it would involve the same conditions as the original rule, but usually a few of the answer choices quickly reveal themselves as incorrect, and then you would only need to work through a couple of answer choices to see which one was technically correct.
Hope that helps!
-Malila

[Tw07]

In response to Kelly's post above, Is there a section on the student portal with modules including worked problems? Or is that in reference to the lesson recaps? I am also struggling with rule substitution and would love to see more examples walked through if that is available somewhere on the site. Thanks in advance!

[Adam Tyson]

Tw07, we don't have any modules that I am aware of that are focused just on working through Rule Substitution questions. Those questions can be found sprinkled throughout every type of game over many different tests, and these days you can expect that at least one of the games will have one (and be grateful for any test that has none!) I think your best bet for improving on this type of question is to tackle game sections from practice tests, try out the concepts we discuss in this forum (like looking for a rule that restates an inference, and focusing on rules that impact the same variables, or groups, or spaces that the removed rule affected), and in the end, find the thread in this forum that discusses the specific question you are struggling with.

For this particular question, I would actually focus on the templates (because this is a great game for doing templates) and as I look at each answer I would ask myself "if the old rule about the 4th floor was removed, would this answer result in the same templates?" Answer E, for example, would recreate one of the templates, but what about the two templates that have the 3rd floor on Wednesday? In one of those cases, I could have put the 4th floor on Saturday, so answer E doesn't recreate the same set of restrictions that I had originally. That makes it a wrong answer.

Rule Substitution questions are a potential thorn in our side, for sure, but if we approach them calmly, willing to invest the time and looking for the right result of recreating the original diagram, we can manage them. Keep at it, and keep coming back here for more help!

[jm123]

For this question, I was in between A and B and ultimately went with B.

Is B incorrect because it says "The fourth floor cannot be examined on an earlier day than the second floor?" I took this statement to mean that 2 must be before 4. However, when I am reviewing, I think it is wrong because it allows for the possibility for 2 to go on the same day as 4, therefore, allowing them both to be on Wednesday and making this answer choice incorrect.

On the other hand, answer choice A is correct because according to this rule, whenever 7 is on Friday, 4 must also be on Friday because it cannot be on the same day as 3. Likewise, when 7 is on Thursday 4 would have to be on either Thursday or Friday. So whatever location you choose for 7, 4 will always be forced into Thursday or Friday.

[Paul Marsh]

Hi jm123! You did a great job of figuring out why (B) is wrong.

(B) allows for the possibility that 2 and 4 could go on the same day, which means that 4 could go on Wednesday. Similarly, it allows for the possibility that 8 and 4 could go on the same day, which means that 4 could go on Saturday. So (B) does not do a good job of substituting in for our rule. (Remember, we're looking for an answer that successfully constrains 4 to Thursday and Friday).

Now let's look at (A). (A) restricts 4 to being on the same day as, or the day before/after, 7. Where can 7 go again? Well, only Thursday or Friday, since it has to come after 3 but before 5 (because of Rules 3 and 4). Let's look at both of those scenarios.

So if 7 is on Thursday, that means 4 would have to go on the same day (Thursday), or the day before/after (so Wednesday or Friday). No problem with 4 going on Thursday or Friday, but if it can go on Wednesday then (A) is not a good answer. Luckily, it can't. Why not? Well, if 7 is on Thursday, then that means 3 has to go on Wednesday (because of Rule 3). And because of Rule 1, 4 can't go on the same day as 3, which means Wednesday's out. So that only leaves the possibility of 4 going on Thursday or Friday.

What about if 7 is on Friday? Well, that means 4 would have to go on the same day (Friday), or the day before/after (Thursday or Saturday). No issues with 4 going on Thursday or Friday. But if it could go on Saturday that would be a problem! It can't though. If 7 is on Friday, that means 5 has to be on Saturday (because of Rule 4). Because of Rule 1, 4 can't go on the same day as 5, so Saturday's not an option. Which leaves only Thursday or Friday for 4.

So (A) only allows for 4 to go on Thursday or Friday, which makes it a great substitute for our rule and a great answer.

Hope that helps!

[Mozart]

Hi,

I have a question about eliminating answer choices with conditional statements in Substitution questions.
Would such an answer choice be wrong if you can come up with different sufficient conditions that allow for the rule to be violated?
In E), if the 3rd floor is on Wednesday (as Adam had said), then we could put the 4th floor on Saturday.
I also looked at E) in terms of the contrapositive: if the 4th floor isn't on Friday, the 3rd floor isn't on Thursday. The 4th floor could then go on Wednesday, thus breaking the substituted rule.

Would this be a good way to look at answer choices with conditional statements?

Thank you so much for your help!

[KelseyWoods]

Hi Mozart!

In Rule Substitution questions, you want a new rule that does not add any additional restrictions to your original diagram, but retains all of the same restrictions. To check conditional statements to make sure that they are not adding any additional restrictions, you should test to see if you can have the sufficient condition without the necessary condition.

So for answer choice (E), if in your original diagram you can have 3rd on Thursday without having 4th on Friday, then it is adding a restriction that you didn't have originally and you should eliminate it. Testing the contrapositive would be the same thing: you'd be seeing if you can have 4th not on Friday and still have 3rd on Thursday.

But remember that testing to see if they are adding any additional restrictions is only one part of testing answer choices in a Rule Substitution question. You also need to make sure it's adding in the restriction that is being substituted.

Hope this helps!

Best,
Kelsey

[hhaugen@ualberta.ca]

Hello!

I am struggling to understand why C is incorrect, I understand that A works, but not why C does not.

Thank you!