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This is an Advanced Linear: Balanced Game.
The setup of this Advanced Linear game is more challenging than the setup of the first game of this section, primarily because although this game appears to have only a few initial inferences, the relationship of the rules is such that most of the diagram can be filled in. With the proper diagram, the questions are relatively easy.
From the game scenario, we know that there are three variable sets: the five archaeological sites, the three archaeologists, and the three centuries. The five archaeological sites and the three centuries each have numerical order, but the archaeological sites are the better choice for the base since each site has a single archaeologist and a single date. This choice creates a linear setup with two stacks, one for the archaeologists and one for the centuries (remember to leave ample vertical space between the two stacks since each row will likely have its own Not Laws):
Because the rules have so many consequences, let’s examine each rule individually.
Rule #1. This rule is the most straightforward rule of the game, and it can be represented by placing a “9” in second site space of the Century row:
Rule #2. If neither the fourth nor fifth site was discovered by O, we can place O Not Laws on each space. And, because there are only three archaeologists, with O eliminated from discovering the fourth and fifth sites we can infer that either F or G discovered those sites. This fact can be represented by individual F/G dual-options on each site:
Rule #3. While the first two rules can be represented directly on the diagram, this rule must be diagrammed separately. The rule is a bit challenging to represent because it contains two separate pieces of information. The first piece of information is that G discovered exactly one site, and the second piece of information is that the site discovered by G dates from the 10th century. There are different ways to represent this rule, but we will use the following diagram:
From the contrapositive of this rule we can infer that any site that dates from the 8th or 9th century was not discovered by G, and must therefore have been discovered by F or O. Also, be careful not to make a Mistaken Reversal and assume that any site that dates from the 10th century was discovered by G; that is not necessarily the case.
Using the information above, we can infer that since the second site dates from the 9th century it was not discovered by G, and must therefore have been discovered by F or O:
Rule #4. This is another important conditional rule, which can be diagrammed as follows:
Operationally, this rule indicates that every time a site dates from the 8th century, it must have been discovered by O. The contrapositive of this rule reveals that if a site was not discovered by O, then it cannot date from the 8th century and must instead date from the 9th or 10th century. Thus, the fourth and fifth sites, which were not discovered by O, cannot date from the 8th century, and they must date from the 9th or 10th century. We can add this to our diagram with dual-options:
Rule #5. Although we have already gained a fair amount of information from the first four rules, the final rule will allow us to fill in most of the remaining spaces in the diagram. First, however, a note about the language used in this rule. In most cases, “either…or” on the LSAT means “at least one of the two, possibly both.” For example, if we see the rule “either A or B must attend,” this means that at least one of the two must be there; they are not both required to attend, but they both could attend. In this particular rule, however, we should note that the word “either” is preceded by the conjunction “than” and is used at the end of a comparison. When this is the case, “either” actually means “both.” For example, “He is taller than either of the other two boys on the team” means that he is the tallest of the three, and, “She likes History better than either Biology or Physics” means that History is her favorite of the three classes mentioned. So, the proper interpretation of this rule is that the third site is more recent than both the first and fourth sites.
Thus, when this rule states that the third site dates from a more recent century than either the first or fourth site, the third site cannot date from the 8th century, and the first and fourth sites cannot date from the 10th century. By itself, this information only seems to result in a series of dual-options for the dates of these sites. However, because we have already concluded that the fourth site must date from the 9th or 10th century (this inference was produced by combining the second and fourth rules), and this rule indicates that the fourth site cannot date from the 10th century, we can conclude that the fourth site dates from the 9th century. And, because the fourth site must date from the 9th century, we can use this rule to determine that the third site must date from the 10th century. Consequently, we can fill in the entire century row with either the exact site dates or with dual-options:
Further, because the fourth site cannot date from the 10th century, from the third rule we can infer G cannot discover the fourth site, and so the fourth site must be discovered by F. We can also use the third rule to determine that the first site was not discovered by G, and must have been discovered by F or O. These inferences allow us to arrive at our final diagram:
Note that not all of the dual-options are independent. For example, if the first site dates from the 8th century, then according to the fourth rule it must have been discovered by O. The third rule is also active, and during the game you must keep track of the placement of G. Regardless, you now have a powerful setup with which to attack the game.
Final Note: the language used by the test makers here only states that each site dates from a particular century, not that every century must be used (the same situation applies to the archaeologists). Thus, it is possible that some variables may not be used in the game. Each game is different, so always track the language used in a game carefully to ascertain the situation.