Who among the following likes grey colour? Study the following information carefully and answer the questions given below:
Six persons –P, Q, R, S, T and U are living on different floors of the six-storey building such that the lowermost floor is numbered as one and the floor immediately above it is numbered as two and so on. Each of them likes different colours- Red, Blue, Grey, Black, Pink and White but not necessarily in the same order. Only two floors are between the one who likes grey colour and U who lives on an odd numbered floor. P lives immediately above U. The number of floors below P is one more than the number of floors above the one who likes white. Only one floor is between Q and the one who likes pink colour. The one who likes Pink colour and the one who likes blue colour live on the adjacent floor. Neither U nor P likes blue colour. The number of floors between the one who likes black and S is two less than the number of floors between S and the one who like red. T likes neither grey nor red.
Correct Answer :
The one who lives on the topmost floor
Solution :
To find out who likes the grey colour, we can reconstruct the floor arrangements and color preferences step-by-step based on the given clues.
Let the floors be numbered from 1 (lowermost) to 6 (topmost).
Step 1: Determine the positions of U, P, and the Grey colour
Clue 1: U lives on an odd-numbered floor (1, 3, or 5).
Clue 2: Only two floors are between the one who likes grey and U.
Clue 3: P lives immediately above U.
Let us analyze the case where U lives on floor 3:
- If U is on floor 3, then P must be on floor 4 (immediately above U).
- Since there are two floors between U (floor 3) and the one who likes grey, the one who likes grey must be on floor 6 (as floor 0 does not exist).
Step 2: Place the White colour
Clue 4: The number of floors below P is one more than the number of floors above the one who likes white.
- Since P is on floor 4, the number of floors below P is 3.
- Therefore, the number of floors above the one who likes white must be:
.
- The floor that has exactly 2 floors above it is floor 4. Thus, the person on floor 4 (P) likes the white colour.
Step 3: Analyze the positions for Pink, Blue, and Q
Clue 5: Only one floor is between Q and the one who likes pink colour.
Clue 6: The one who likes pink and the one who likes blue live on adjacent floors.
Clue 7: Neither U nor P likes blue.
- Since P (floor 4) and U (floor 3) do not like blue, blue cannot be on floor 3 or 4.
- Since U is on floor 3, let's assume U likes pink. Under this assumption, the one who likes blue must be on floor 2 (adjacent to floor 3, since floor 4 is already White). This satisfies the condition that neither P nor U likes blue.
- Since U (floor 3) likes pink, Q must be on floor 5 (leaving exactly one floor, floor 4, between Q and the pink colour).
Step 4: Analyze the positions of Black, Red, and S
Clue 8: The number of floors between the one who likes black and S is two less than the number of floors between S and the one who likes red.
- Currently, the colors placed are: Grey (floor 6), White (floor 4), Pink (floor 3), and Blue (floor 2). This leaves Black and Red to be distributed between floor 1 and floor 5.
- Let S be on floor 2 (who likes Blue).
- If Black is on floor 1 and Red is on floor 5:
- Number of floors between Black (floor 1) and S (floor 2) is 0.
- Number of floors between S (floor 2) and Red (floor 5) is 2 (floors 3 and 4).
- Since , this perfectly satisfies the condition.
Step 5: Determine the final arrangement
- Since Red is on floor 5 and Black is on floor 1, and T likes neither grey nor red, T must be on floor 1 (liking Black).
- Q is on floor 5 (liking Red).
- The remaining person R must be on floor 6 (liking Grey).
This gives us the complete final table:
Floor 6: R (Grey)
Floor 5: Q (Red)
Floor 4: P (White)
Floor 3: U (Pink)
Floor 2: S (Blue)
Floor 1: T (Black)
From the arrangement, the person who likes the grey colour lives on floor 6, which is the topmost floor.
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