Which one of the following could be true?

on October 26 at 06:06PM

Explanation please

I don’t know how to arrive at the answer for this one

1 Reply

Irina on October 26 at 11:55PM

@hannahnaylor5,

This is a challenging question, (A) should jump out as one of the likely answers but an alternative would be to to start by eliminating the wrong answers. Every answer that involves three employees getting their 2d/3d/4th choice is implausible, let's consider each of these wrong answers.

Each employee selects only one office and cannot select an office selected previously, we see that 3 out of 4 employees chose W as their 4th choice and 1 chose Y as their 4th choice. If three employees were to select an office that they ranked 4th, we would end up with at least two employees in office W, which would violate the rules, hence we can eliminate (E).

Exactly three of the employees select their third choice. The third choices are Z W X Z - we cannot have two employees in the same office, so it would have to be offices Z W X, but X is also the first and second choice for three out of four employees, meaning X will definitely get picked before anyone's third choice, even if it is picked third. Let's say J goes first and picks Y his first choice, P goes second and picks Z his second choice, then T or L will necessarily pick X because it is their first choice. We can thus conclude that (D) is impossible.

Exactly three employees each select the office they rank second. Well this scenario could only be possible if everyone had the same first choice and three employees had different second choices. Since X and Y are both first choices, we can conclude that at least two of the employees get their first choices so at most two could get their second. Hence, we can eliminate (C).

Exactly two of the employees each select office they rank forth. Since we have three employees choosing W and one choosing Y as their fourth choice, the offices selected must be W and Y but Y is two employees first choice so it will definitely get picked before anyone's forth choice, meaning we can eliminate (B).

Exactly two of the employees each selects an office ranked third. Consider this scenario:
T goes first and selects his first choice X.
P goes second and selects his first choice Y.
J goes third and since X and Y are taken, he gets his third choice Z.
L goes last and since X and Z are taken, he gets his third choice W.

Since it could be true that two employees get their third choice, (A) is the correct answer.

I would definitely start with checking if (A) could be true on a real test, and since we can quickly come up with a scenario where two of the employees get their third choice, we could select (A) and move on.

Let me know if this helps and if you have any further questions.