Who among the following lives on 4th floor? 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 likes white
Solution :
To find the person who lives on the 4th floor, we can analyze the given information step-by-step:
1. Determine the positions of U and P:
We are given that the building has six floors numbered 1 (lowermost) to 6 (uppermost).
U lives on an odd-numbered floor, so U can live on floor 1, 3, or 5.
P lives immediately above U. This gives us three possible cases:
- Case 1: U lives on floor 1, and P lives on floor 2.
- Case 2: U lives on floor 3, and P lives on floor 4.
- Case 3: U lives on floor 5, and P lives on floor 6.
2. Analyze the relation between U and the one who likes Grey:
There are only two floors between U and the one who likes grey.
- In Case 1 (U on floor 1), the one who likes grey must live on floor 4.
- In Case 2 (U on floor 3), the one who likes grey must live on floor 6.
- In Case 3 (U on floor 5), the one who likes grey must live on floor 2.
3. Analyze the relation between P and the one who likes White:
We are told that the number of floors below P is one more than the number of floors above the one who likes white.
Let be the number of floors below P, and be the number of floors above the white-colour-liking person. The relation is:
Let us test this relation for our cases:
- In Case 1: P is on floor 2.
The number of floors below P is 1.
Applying the relation: .
This means the one who likes white lives on the top floor (floor 6).
- In Case 2: P is on floor 4.
The number of floors below P is 3.
Applying the relation: .
This means there are 2 floors above the one who likes white, placing the one who likes white on floor 4.
- In Case 3: P is on floor 6.
The number of floors below P is 5.
Applying the relation: .
This means there are 4 floors above the one who likes white, placing the one who likes white on floor 2.
4. Identify the floor 4 occupant:
In Case 2, P lives on floor 4, and the color liked by the person on floor 4 is white. Hence, the occupant of the 4th floor is "The one who likes white".
This directly matches one of our options: The one who likes white.
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