The President of a club is appointing nine officials - J, K, L, M, N, O, P, Q and R - to serve on the study three committees to study three different aspects of activities at the club. There will be a Games Committee, a Food Service Committee and an Entertainment Committee. Her appointments must respect the following:
i) Each comummittee must have exactly three members.
ii) No person can serve on more than one committee.
iii) Q must serve on the Entertainment Committee.
iv) L and M must serve on the same committee.
v) J and K cannot serve on the same committee.
vi) N cannot serve on the same committee as R.
vii) O must serve on the same committee as K or Q or both K and Q.
If R is on the Entertainment Committee and K is on the Food Service Committee then which of the following must be true?

Options

A. O is on the Entertainment Committee.
B. L is on the Games Committee.
C. P is on the Food Service Committee.
D. O is on the Games Committee.

Answer

B

Explanation

Here, is another selection set. Begin by summarising the information :
Q = Entertainment
L = M
`J ne K`
`N ne R`
O = K or Q or both
You may want to diagaram this :
`{:("FS E G"),("K QR"):}`
Next, try placing L and M together. If you put L and M on the Food Services Committee then O must be on the Entertaiment Committee (to respect the last condition), which places both N and R on the Games Committee- in violation of the fourth condition. Since L and M cannot go the Enterinment Committee, they must go the Games Committee :
`{:("FS E G"),("K QR LM"):}`
Now, it doesn.t seem possible to assign the other members to a specific committee. O could go either with K or with Q, and J and K and N and R could go to any committee—so long as we separate them. Is this enough to answer the question, however? Yes. Our diagram confirms that (2) is necessarily true.