### IIFT 2018 Question 26

Instructions

Based on the information below, answer the questions which follow.

Richie invites three of his friends Sunny, Pinky and Nancy for his birthday party organised at his home. As the party goes on till late in the night, Sunny, Pinky and Nancy choose to stay at Richie's house. Being good friends they usually stay back at each other's house. Each one of them including Richie stay either in the room painted blue or in the room painted purple. They have adequate number of rooms of both colours. The preferences which need to be fulfilled are:

i. If Sunny stays in the room painted purple, then Pinky and Richie stay in the same room as Nancy.

ii. If Pinky stays in the room painted purple, then Sunny stays in the room in which Nancy and Richie don't stay.

iii. if Nancy stays in the room painted blue, then Sunny and Richie stay in the room which Pinky has chosen.

iv. If Richie stays in the room painted Blue then Sunny and Pinky do not stay in the same room as Nancy.

Question 26

# Under all possible combinations which of the two friends will always have their room colours unchanged.

Solution

(i) S -> Purple
P,R,N -> Purple (or) P,R,N -> Blue
(ii) P -> Purple
S -> Blue  N,R -> Purple (or) S -> Purple N,R -> Blue
(iii) N -> Blue
P,R,S -> Purple (or) P,R,S -> Blue
(iv) R -> Blue
S,P -> Blue N -> Purple (or) S,P -> Purple N -> Blue
Let us consider N is in blue, then P, R, and S should be either in blue or purple.
If N is in blue and (P,R,S) is in blue, then this doesn't satisfy the condition in statement 4. If N is in blue and (P,R,S) is in purple, then this violates statement 2. Therefore, N cannot be in blue and stays in Purple room.
Let us consider S is in purple, then P, R, and N should in purple as N cannot be in blue.
If S is in purple and (P,R,N) is in purple, then this violates statement 2. Therefore, S cannot be in purple and stays in Blue room.
Possible arrangements are:
1. P - purple, S - blue, (N,R) - purple
2. R - blue, (S,P) - blue, N - purple
Rooms of N and S are unchanged in all the cases.

• All Quant Formulas and shortcuts PDF
• 40+ previous papers with solutions PDF