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#78485
Complete Question Explanation

The correct answer choice is (E).

Answer choice (A):

Answer choice (B):

Answer choice (C):

Answer choice (D):

Answer choice (E): This is the correct answer choice.

This explanation is still in progress. Please post any questions below!
 arjanlion@gmail.com
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Hey PowerScore,

I found this question to be super hard, and was quite lost on it.

Any help would be appreciated. Thanks!
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 Beatrice Brown
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#89066
Hi Arjan! Thanks so much for your question. This is definitely a tricky pattern game.

In question 16, we're given an additional condition since this is a local question, and we're then asked which of the answer choices could be true. In other words, we want to find which answer choice doesn't lead us to violate any of the rules.

What we know from the condition given is that P selects W, which is P's last choice. From the rules, we know that any of the employees selects the office that they ranked highest of those that have yet to be selected. If P selects W, then that means that Y, Z, and X (ranked 1-3) all must have already been selected since P is selecting their last choice. Having made this inference, we can turn to the answer choices and figure out which of the answer choices allows P to select W (meaning the answer choice will make it such that Y, Z, and X have already been taken by a different employee) without violating any other rules.

Answer choice (A) cannot be true. If two of the employees picked their second choice, then two of J, L, or T would have to pick their second choice. If J and L pick their second choice (J picks X and L picks Z), then that means Y has to be selected by T. But Y is also T's second choice, and according to the rules, at least one employee must get their first choice. If J and T pick their second choice (J picks X and T picks Y), then that means L must pick Z, which is their second choice, which means that no employee gets their first choice and violates the rules. If L and T pick their second choice (L picks Z and T picks Y), then J must pick Z, but that's J's third choice, meaning that no employee picked their first choice (which violates the rules).

Answer choice (B) also cannot be true. If two of the employees pick their third choice, then two of J, L, or T would have to pick their third choice. But this isn't possible, as either L needs to pick W (which we know is picked by P and therefore violates the rules since each must select a different office) with J or T picking Z, or J and T need to pick their third choice (which is the same and therefore would violate the rules).

Answer choice (C) cannot be true because that would mean that J, L, and T all pick their first choices. But L and T have the same first choice of X, so if they both get their first choice, this violates the rules since each employee must pick a different office. Additionally, Z would be left unselected since it's not one of J, L, or T's first choices, which would also violate the rules.

Answer choice (D) cannot be true because if J selects X, that means that Y must have already been selected by either L or T because someone else must have taken J's first choice (Y) if they are picking their second choice. But Y is L's last choice, and Y is T's second choice, which means that none of the employees would have gotten their first pick and this violates the rules.

Answer choice (E) can be true and is therefore correct. If L picks Z, then that means someone else picked X (L's first choice). If T picks X, they get their first choice. J can also then get their first choice and pick Y. So this is a scenario that can be true! J and T get their first choices, L gets their second choice, and W gets their last choice since Y, Z, and X are picked by the other employees.

Again, this is a tricky game! The best way to approach this particular question is to figure out what has to be true from the condition given in the question (that Y, Z, and X must all be picked by the other employees) and to then see which answer choices violate vs. don't violate the rules.

I hope this helps, and let me know if you have any other questions!

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