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 Adam Tyson
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#93976
Hey Owl, happy to help clear that up for you! The GH block in this situation is a Necessary Condition wherever you place a G. It's not that H and G must always go together, because H can (and in fact, must) be placed in a group that does not include G. It's "If you have a G, then you must have a GH block." The contrapositive, then, would be "anywhere that does not have a GH block cannot have a G."

Things would be different if the rule told us that G and H must always be together, like "G and H must learn the same languages as each other" or "G learns any language that H learns and vice versa." For those you would get that double arrow or fixed block you asked about.
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 Stephanie Oswalt
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#97164
Hello,

We received the following question from a student:

"I am having difficulty understanding your explanation "Since H, L & P each learn Yoruba, it seems likely that any combination of two of those three researchers could learn Swahili. Since answer Choice C D & E each list two of H,L or P it seems unlikely that any of those answer choices are correct. Why is it unlikely? the question is so non- specific and doesn't limit the number of researchers who could learn a # of languages in this question that several of the other choices besides B could correctly answer this question. Please explain further. "

An instructor will respond below.
 Luke Haqq
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#97182
Happy to break apart the explanation above.

First, the explanation mentions answer choices that are likely or unlikely based on a non-specific question. The question stem asks which of the answer choices "could" be true, in combination with the word "except." In other words, four of the answer choices could be true, but one cannot be true. By mentioning answer choices that appear likely or unlikely, the above explanation seems to be offering a strategy in terms of how to tackle this question and others like it expeditiously. For example, if one encounters a could-be-true question on a game and the game has a random variable, the right answer choice is likely to have that random variable in it. In this question stem, however, we have could-be-true plus the "except." Four of the answer choices could be true, and correct answer choice based on the question stem cannot be true.

Second, let's look closer at the first two sentences.

Since H, L & P each learn Yoruba, it seems likely that any combination of two of those three researchers could learn Swahili.
How do we know that H, L, and P each learn Yorba? This is because (1) there's a rule that exactly 3 researchers learn Yorba, and (2) there is a rule preventing G from learning the same language as L and P. Because of the latter constraint, we know the specific 3 researchers out of the 4 who learn Yorba: H, L, and P. Knowing that H, L, and P all can learn the same language in at least one case without violating any rules is why it seems "likely" that they could all learn another language such as Swahili without necessarily violating any rules.

Next we have:

Since answer Choice C D & E each list two of H,L or P it seems unlikely that any of those answer choices are correct.
As mentioned above, the explanation both seems to be about how to arrive at the correct answer, and also how to do so as quickly as possible. Since four of the answer choices could be true, this sentence suggests that answer choices (C), (D), and (E) on their faces all look like they could be true. These three answer choices are all different permutations of H, L, or P being together, which we saw doesn't violate any rules at least in the case of Yorba. This isn't necessarily a reason to completely eliminate these answer choices, but it at least strongly suggests looking to the other ones.

This leaves us with answer choices (A) and (B) as contenders. Given the question stem, 4 answer choices could be true but the correct answer choice cannot be true. A good first instinct in determining which answer choice cannot be true would be to search for one with the geologist--since this is the variable with the most restrictions. Of course, the geologist isn't in any of the answer choices, so this doesn't tell us which of (A) or (B) is the correct answer. We can therefore try out both answer choices, which is a much more manageable task if one is only doing so for two of the answer choices rather than all of them.

We're asked for "a complete and accurate list of the researchers who learn both Swahili and Yoruba EXCEPT," and answer choice (A) is "the historian." We can diagram this out, using a base like the following:

R: _
S: _ _
T: _ _
Y: _ _ _

Can answer choice (A) be true? We can put in H as the only one of the researchers who learns both S and Y:

R: _
S: H _
T: _ _
Y: H _ _

It seems like (A) could be true. For example, H and G could both learn Swahili, and H, L, and P could learn Yorba (actually, we know it must be true that these 3 learn Yorba, as noted above):

R: _
S: H, G
T: _ _
Y: H, L, P

We don't necessarily need to figure out who learns Rundi or Tigrinya. The above seems sufficient to show that it could be true that the historian is the only one who learns both Swahili and Yorba.

Finally, consider (B), "the paleontologist" is the only one who learns both Swahili and Yorba:

R: _
S: P _
T: _ _
Y: H, L, P

So far, so good. But who else can fit in that slot as the second researcher who learns Swahili? It wouldn't work to put L in this slot, since that would violate the condition of this question that P is the only researcher who learns both Swahili and Yorba. For the same reason, it wouldn't work to have H learn Swahili with P. As with L, H is already learning Yorba. Lastly, it wouldn't work to have G with P learning Swahili either, given that one of the rules prevents G and P learning the same language. We need a second researcher to learn Swahili with P, given the rule that 2 people learn it, but there is no one who can learn it with P under the localized conditions of this question.

Thus, it cannot be true that "the paleontologist" is a complete and accurate list of the researchers who learn both Swahili and Yorba. Since this cannot be true, we know that it is the correct answer choice given the could-be-true/except question stem.

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