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 Dave Killoran
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#45764
Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=8976)

The correct answer choice is (B)

This is the defining question of the game. From the language in the question, it is clear that one of the five variables listed in the answer choices must always be advertised during the second week, yet prior to this question very few students realize that one of the products must always be advertised during week 2. Answering this question correctly is crucial since this information will definitely impact your ability to answer the subsequent questions both quickly and accurately.

The easiest way to attack this question is to again use the information from the hypothetical created in question #18. From answer choice (B) in that question, it is certain that either J or G must be the product advertised in week 2. Let us stop and take a moment to analyze this critical insight. First, as indicated by the question stem to #20, you now know that one of the products will always be advertised on week 2. If you did not discover this inference previously (and most people do not), you know you are missing a key piece of information that will undoubtedly help you solve not only question #20, but other questions as well.

When you know that one of the products must be advertised on week 2, then you can deduce that every single solution to the game will contain that product on week 2. This is a vital point since you can then look at any other hypothetical and immediately know that one of the two products listed on week 2 will be the one that is always on week 2. So, in question #18, when we determine that (B) is the correct answer, we know that either J or G must be the product that is always on week 2, and we can then look at only J or G in question #20. If there were other hypotheticals we could look at those also, and we would see that either J or G would always be present. For example, if another question produced J and K on week 2, this would show G does not have to be on week 2, and G would be eliminated from consideration; since J would be the only common variable between the two hypotheticals, then J would be proven correct. Thus, even though question #18 lists just one possible schedule of ads (“could be” a schedule of ads) it will still contain the product that we know from the wording of question #20 must always be on week 2.

Another way of thinking about questions #18 and #20 would be to say that if a product must always be advertised on week 2, and then if it does not appear on week 2 in one of the solutions, then how can that particular product be the one that is always on week 2? Therefore, any product not on week 2 in the solution to question #18 is immediately eliminated as the product that must always be advertised on week 2 (for example, if (D) was the answer to #20, then L would be in every solution to the game. But L is not in the solution to #18, so how could it be L?).

In applying this thinking to similar questions in other games, whenever you encounter a question that indicates that a variable must be in a certain group or position, then every other solution to the game will contain that variable in that position. So, if a question asks, “Which one of the following people must always be in the first group of runners?” and the correct answer to another question indicates that W, X, and Y are the only runners in the first group, then you would automatically know that one of W, X, and Y would have to be the runner that is always in the first group. Similarly, if a question asks, “Which one of the following must always be the third factory inspected?” and the correct answer to another question indicates that P is the third factory inspected, then you would automatically know that P is always the third factory inspected.

Returning to our consideration of G and J from question #18, the fact that one of those two must be the correct answer eliminates answer choices (C), (D), and (E) in question #20, once again demonstrating how important it is for you to answer List questions correctly and then use their information when applicable. Now that the contenders have been narrowed to two, you can easily make a hypothetical that proves or disproves one of the answers. Let us begin by attempting to prove that G does not have to be advertised in week 2 (it is almost always easier to disprove a Must Be True statement than prove it). The following hypothetical proves that answer choice (A) is incorrect:
d96_Game_#4_#20_diagram 1.png
Since answer choice (A) can be disproved, it follows that answer choice (B) is correct and J must be advertised during week 2. We can then infer that H must be advertised during week 1 (Why must H be advertised during week 1? Because in this question we discover that J must be advertised during week 2. Adding that piece of information to the first rule of the game then leads us to the inference that H must be advertised during week 1).

Adding these new inferences and Not Laws, we arrive at the following optimal setup for the game:
d96_Game_#4_#20_diagram 2.png
Note that H cannot be advertised in weeks 2 or 3 due to the second rule (that is, if H is the doubled variable it would have to be in 1-4). J cannot be doubled since that would also require H to be doubled—a violation of the rules. Therefore, J can be eliminated from weeks 1, 3, and 4. Since G must be advertised with either J or O, and J and O cannot be doubled, G must be advertised during week 2 or 3, and thus G cannot be advertised during weeks 1 or 4.

The above setup is optimal and should be used for all subsequent questions. Of course, you would want to check the previous questions to make sure you have not made any errors.

Perceptive students may have noticed another way to disprove answer choice (A) in this question. If G is advertised during week 2, then automatically J must also be advertised during week 2, since G must be advertised with either J or O, and O cannot be advertised during week 2. Since selecting answer choice (A) would automatically make answer choice (B) correct, answer choice (A) must be incorrect since there can be only one correct answer.

An additional note on the difficulty of this game: the importance of the inference contained in this question is reflected in the very nature of the questions themselves. Six of the seven questions in this game are Global, which means that most of the questions are based on information derived from the initial setup. If you miss this one key inference or never answer this question, you are automatically at a disadvantage in answering the rest of the questions. In other words, if you skip this question, you are passing on a chance to discover a major inference that applies to every other question.
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 pacer
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#17120
I am confused about question 20.

Here is my reasoning:

From my main diagram, since O is in week 3, then G could be in the week preceding either O or J. So, why can't G not be in week 2? By placing G in week 2, the HJ block would have to go in weeks 3-4. And since H is in week 3, it cannot be doubled and thus, J cannot be doubled.

If I place J in week 2, then H must be in week 1. This allows for the possibility for H and/or J to be doubled.

My attempt to these questions is to make a hypothetical for the choice remaining and see if that violates any of the rules. In this case, I am stuck between answer choices A and B.

Also, I have a general question:

For example, in this question, I was able to eliminate choices C, D and E based on the answer choice I had selected for question 18 (a list question). This is also explained in the solutions. But in case I had done question 18 wrong, how should I go about solving this question?
 Emily Haney-Caron
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#17123
Hi Pacer,

The fastest way to approach this one is definitely to use your answer from question 18; as you identified, since 20 is asking which one MUST be advertised during week 2, and question 18 shows a possible solution where G and J are advertised during week 2, we can narrow it down to one of those two and eliminate answers C, D, and E. Given the time constraints, this is a situation where you probably want to rely on that earlier answer to answer this one quickly.

We know J cannot be in 1 because of the first rule. J also cannot be in 3, because then O and J would both be in 3, and therefore one would need to be doubled to go with G - but the products in week 3 cannot be doubled. If J is in 4, H has to be in 3, because of the first rule, which means that G has to go with J in week 4 (J can't be doubled, since that would require a second H, as well, and O is already in week 3 with H). That would mean either G or J has to be doubled, since they would be the only two in week 4, but neither of them can be without also doubling a second product (which violates the rules). Therefore, J cannot be in weeks 1, 3, or 4, so we know it MUST be in week 2.

I hope that helps!
 Echx73
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#22567
Hey Team,

I am having problems understanding your thought process on how you deduced J must be advertised during week 2!?
I understand how we can look back to Q18 and see that J & G "could" be there, but how do I not know other products could go in week 2 as well? Thank you for your help as always!

Eric
 Clay Cooper
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#22576
Hi Eric,

Thanks again for another great question. This inference is a little hard to see, so let's take it step by step.

According to the setup and the rules, J is advertised at some point - for all we know at the beginning of the setup, possibly even twice. However, our first rule tells us that J is not advertised unless H is advertised in the immediately preceding week - that means that J can't be advertised in the first week, since there is no immediately preceding week.

J also cannot be advertised in the third week, because we are told that the letter that is repeated does not appear in the third week. This means that placing J in the third week with O would result in both of them being completely used up, which would leave G without a partner, since he can only pair with J or O - thus J cannot be advertised in the third week.

Finally, J also cannot be advertised in the fourth week. In order for J to be advertised in the fourth week, it would have either to be the product that is repeated or not the product that is repeated. However, neither is possible; J cannot be repeated because doing so would require repeating H as well (since it must always immediately precede J) and that would require two repeats, which is against the rules; furthermore, if J were the product in the fourth week that is not repeated, that would mean that H would have to precede it in week 3 with O - thus filling up week 3 and again leaving us with no eligible partners for G, since week 3 is now full and G can't be the repeated variable in week 4 if J and O are completely used up.

Does that clarify? I hope so - J must appear in week 2 because he must appear somewhere and the other weeks can all be eliminated as possibilities.
 Echx73
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#22587
Hey Team,

I totally understand now! The thing that was messing me up was the whole reference about looking back to Q18. Of course, Q18 has to have one of the products that must be in week 2! In addition, if I was in the middle of a real test I could have just started to grab answers and deduce!

Eric

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