This game involves a company with five employees - F G H K L, each of them holds one of three positions - P M T. P is the only one unsupervised, other are supervised by exactly one employee who is either P or M. Each supervised employee holds a different position from tat of his supervisor, i.e. a manager cannot supervise another manager. The rules tell us that:
(1) There is exactly 1 president (2) At least 1 of the employees that president supervises is a manager (3) Each manager supervises at least one employee This rule allows us to infer that there cannot be more than two managers since we have five employees total and one of them is president:
1P -2M -2T
we could alternative have only 1 manager, resulting in the following scenario:
1P-1M -3T
(4) F does not supervise any employee. This rule allows us to infer that F is a technician, since the president and any manager must supervise at least one employee.
F-T
(5) G supervises exactly two employees. This rule allows us to infer that G must be either the president or one of the managers, and if he is the manager, then there are no other managers.
The question asks us if K supervises exactly two employees, which of the following must be true?
So now we have a scenario where G supervises 2 employees, and K supervises two employees. It is impossible for two managers each to supervise two employees since each employee is supervised by exactly one employee, i.e. we cannot have 1 technician supervised by two managers, and we only have 5 employees total. It must be true then that one of them is the president and the other is a manager, and since a manager in this hypothetical supervises two employees, we can conclude that there are no other managers, resulting in the following combination of roles:
1P -1M - 3T G & K could switch places in terms of who is the president and who is the manager, but we know that F H L are all technicians.
Since we know that L is a technician, we can conclude that he must definitely be supervised as (C) correctly states.
(B) could be true but it does not have to be true. This hypothetical allows for two scenarios:
G - president K -manager F H L -technicians
or
K- president G- manager F H L -technicians
Since it could be true that G is a manager or it could be false and he is the president instead, we can conclude that (B) is false. Remember that the correct answer choice to a must be true question must be true in every possible scenario.
Let me know if this makes sense and if you have any other questions.
