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#40011
Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=12912)

The correct answer choice is (C)

This is the infamous Rule Substitution question, a staple in the Logic Games section as of late. Considering their growing popularity, tackling such questions is no longer merely optional: it is imperative to have a workable strategy in place. Although the difficulty of this question may have been compounded by the fact that it was the final question in the section, a closer look reveals that the correct answer choice (C) is a straight restatement of the rule in question. Do not assume that the Rule Substitution question will necessarily be difficult! If you skip such questions by default, you may be robbing yourself of an easy point.

The question stem asks you to replace the fourth rule of the game, according to which if K is not assigned to Thorne, then both H and M must be assigned to Thorne:
PT74 - Game_#4_#23_diagram 1.png
Our job is to substitute that rule with a logically equivalent condition, which would have the exact same effect on the order in which the houses are shown. While the wording of the correct answer can be difficult-to-impossible to predict, the four incorrect answer choices will either present rules that were not part of the original rule set (also known as Additional Effects conditions), or else they will only partially constrain the variables in the rule being substituted (i.e. Partial Match conditions).

Since Additional Effects are easier to spot, look for answer choices that contain such conditions first. Unfortunately, none of the answer choices contains Additional Effects.

Answer choice (A): This rule establishes the following conditional relationship between K, H, and M:
PT74 - Game_#4_#23_diagram 2.png
This relationship is true given the original rule, according to which K’s assignment to Silva requires H and M to be assigned to Thorne, and not to Silva. The rule in answer choice (A), however, requires a lot less than the original rule: according to the former, as long as H and M are not both assigned to Silva, the rule is satisfied. This leaves open the possibility that one of H or M is assigned to Silva but not the other, or else that one of them is unassigned. Both possibilities are explicitly ruled out by the original rule. Furthermore, unlike the original rule, the sufficient condition in answer choice (A) fails to specify what must be true if K is unassigned. For these reasons, answer choice (A) contains a Partial Match and is therefore incorrect.

Answer choice (B): This rule establishes the following conditional relationship:

  • ..... ..... ..... ..... ..... K S :arrow: L S
This condition is true given our original diagram, as shown in Template 1. However, it does not require both H and M to be assigned to Thorne, which the original rule did. For instance, the following setup would be possible if we substituted the fourth rule for the rule in answer choice (B):
PT74 - Game_#4_#23_diagram 3.png
Furthermore, unlike the original rule, the sufficient condition in answer choice (B) fails to specify what must be true if K is unassigned. For these reasons, answer choice (B) is a Partial Match condition, and is therefore incorrect.

Answer choice (C) is the correct answer choice. This rule establishes the following conditional contrapositive (we jumped right to the contrapositive for the sake of convenience):
PT74 - Game_#4_#23_diagram 4.png
This condition is consistent with our original inference that F, H, and M must all be assigned to Thorne if K is not. Answer choice (C), therefore, does not contain an Additional Effects rule. The better question is: does answer choice (C) contain a Partial Match? It does not, because F and H must be assigned to the same group as each other (first rule). Thus, the effect of this rule is identical to that of the original rule, and both lead to one and the same inference:
PT74 - Game_#4_#23_diagram 5.png
Answer choice (D) establishes the following conditional relationship:
PT74 - Game_#4_#23_diagram 6.png
This relationship is clearly true given the original rule set, because whenever K is in Silva, H and L are not assigned to the same ceremony as each other. See Template 1. And inversely, whenever H and L are together, K is in Thorne (Templates 2A and 2B). However, unlike the original rule, the sufficient condition here does not mandate that H and M are both assigned to Thorne. For instance, the following hypothetical setup would be possible with this restraint in effect:
PT74 - Game_#4_#23_diagram 7.png
Answer choice (D) is therefore a Partial Match condition, and is incorrect.

Answer choice (E) establishes the following conditional relationship:
PT74 - Game_#4_#23_diagram 8.png
This condition clearly falls short of the original mandate requiring both H and M to be assigned to Thorne. Thus, answer choice (E) is also a Partial Match condition.
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 Sophia123
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#46569
Hi just a quick question on this - I was a little confused because it was my understanding that with an unless statement, the item being referred in the “unless” portion of the statement became the necessary condition. So in this case I thought for C, Kt was the necessary condition and Fs and Ms were negated in the sufficient condition. Does the fact that there’s a “must” in the statement change how an unless statement is diagrammed?
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 Dave Killoran
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#46674
Sophia123 wrote:Hi just a quick question on this - I was a little confused because it was my understanding that with an unless statement, the item being referred in the “unless” portion of the statement became the necessary condition. So in this case I thought for C, Kt was the necessary condition and Fs and Ms were negated in the sufficient condition. Does the fact that there’s a “must” in the statement change how an unless statement is diagrammed?
Hi Sophia,

Thanks for the question! What's shown in (C) above is the contrapositive of the rule, but there should be a note there indicating that. Not sure why there isn't so I'll add one :-D

Thanks!
 Sophia123
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#46740
Got it, thanks Dave! Just to clarify on C then - when negating the portion that goes into sufficient condition of the regular diagram (k and m), the “and” must be changed to an “or” in addition to negations being added to both terms in order to arrive at the contrapositive that is diagrammed above?

Thanks in advance!

Sophia
 Adam Tyson
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#46832
Correct, Sophia! The negation of "both must" is "if at least one of them is not". That translates to "if F is not or if M is not". Good job!
 Sophia123
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#47338
Thank you!
 mahsan
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#62502
I need a little clarification on how answer choice D is diagrammed. Shouldn't the diagram that is listed as the contrapositive be the original conditional statement that the answer choice has described? I know both diagrams ultimately convey the same meaning, so it has no effect on selecting the correct answer, but I want to make sure I'm diagramming conditional statements and their contrapositives correctly.
 Charlie Melman
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#62507
Hi Mahsan,

The statement in answer choice (D) is diagrammed that way because it follows the flow of answer choice (D) itself. When we see a statement that says, "Unless X happens, Y will not happen," it tends to be easiest to translate that as:

(Not) X :arrow: (Not) Y.

What I then like to do is exactly what you thought to do: take the contrapositive to get rid of the double negative.

Y :arrow: X.

All this is to say that answer choice (D) is diagrammed this way in the first instance for convenience.
 Leela
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#65036
Hi!

Is there a good way to attack rule substitution questions that's faster than diagramming all or most of the answer choices? I find this to be a bit of a time suck.
 Rachael Wilkenfeld
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#66861
Hi Leela,

I generally still prephrase substitution questions. In this case, I looked at the original rule: If K is not in T, H and M are in T. That would put F in T as well because F and H are assigned together.

That means that I'm looking for an answer choice that tells me if K is not in T, M and either H or F are. It doesn't matter if it says F or H because one will pull in the other. Personally, I drew out the conditional that I was looking for, to make it easier to spot the correct answer.

We can eliminate answer choices (A) and (B) quickly, because K in Silva doesn't match our conditionals. K in Silva is not the same as K is not in T. It's more narrow than we are looking for, and we cross those out fast. Answer choices (C), (D), and (E) all seem possible with regard to K, so let's look at the other variables. Answer choice (C) talks about K, F, and M. That's a pretty good variable set, so I'm keep it. Answer choice (D) talks about K, H (which would get us F) and L. M isn't addressed, so we can eliminate it. Answer choice (E) talks about K, H or M. I'm going to want to look closer at this one too.

Notice that we've eliminated 3 choices without drawing out any of the answer choices. That gives us a 50/50 shot at this one, even if we run out of time to diagram the 2 answer choices we are considering.

With answer choice (C), we have an unless, so we have to use our unless equation. The answer choice means that if F or M are not in T, then K is in T. If I take the contrapositive, I get if K is not in T, F and M are in T. That looks really close to my prephrase. It would give us F, M, and H in T when K is not in T.

With answer choice (E) we also have an unless to diagram. It says that if K is not in T, either F or M are. That's not enough. We need both M and one of F and H. We can eliminate this one.

Ultimately, with suspension questions, prephrasing will cut down on your work quite a bit.

Hope that helps!
Rachael

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