# Which one of the following is a possible matching of employees with the offices they select?

on November 13, 2018

How is B correct?

How is B the correct answer? I understand the set up but I am not understanding how B is right. Thank you!

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Jacob on November 14, 2018

I find the easiest way to answer this sort of question is to knock off answers by process of elimination by simply applying them to the rule set.

Because there are no repeat offices in any of the answer choices, the only relevant rule is that each employee selects the office that he or she ranks highest among the unselected offices. So letâ€™s use that rule to look at answers.

You should notice right off the bat that the question is not telling you anything about the order of selection â€” so we have to figure that out via inference. In other words, is there an order that works and still follows our rule set?

Answer A: We know that Y is the first choice for J and P, and X is the first choice for L and T. Nobody picked their first choice, so we know this answer is wrong.

Answer C: Same problem.

Answer D: Here, J picked Y, so J is 1 â€” J, and nobody else, got their first choice. We know if L or T were second, they would pick X, since it is their first choice and still available. So P must be second. But Pâ€™s second choice is Z, which was also still available â€” and P didnâ€™t choose that. So this answer is wrong.

Answer E: Same problem.

So B must be right! Letâ€™s work it through:

L got X, their first choice, and nobody else got their first choice, so L must be 1. J or P did not get Y, so T must be second. Tâ€™s second choice was Y â€” fits again! So we now just have J and P left. J has Z, which fits as a third choice, and P has W, which was his 4th. So it all works. This answer is correct.

I hope that helps!