Study the following information carefully and answer the questions given below-
Ten persons P to Y live in 10 storey building but not necessarily in the same order. The bottommost floor is numbered as 1 and so on till the topmost floor is numbered as 10.
V lives on prime numbered floor but below 4th floor. S lives below V but not on the ground floor. There are as many persons live above S as below P. More than three persons live between P and Y who lives above X. One person lives between T and Y. W lives just below R. U does not live below Q.
Who lives on the topmost floor?
Correct Answer :
U
Solution :
To find who lives on the topmost floor, we can step-by-step determine the floor arrangement of the ten persons (P to Y) on the 10-storey building (numbered 1 to 10 from bottom to top) based on the given clues:
Step 1: Determine the positions of V and S.
- Clue: "V lives on a prime numbered floor but below 4th floor."
The prime numbers below 4 are 2 and 3. Therefore, V lives on either floor 2 or floor 3.
- Clue: "S lives below V but not on the ground floor (floor 1)."
If V lived on floor 2, S would have to live on floor 1, which contradicts the condition that S does not live on the ground floor.
Thus, V must live on floor 3, and S lives below V on floor 2.
Step 2: Determine the position of P.
- Clue: "There are as many persons live above S as below P."
Since S lives on floor 2, there are 8 floors above S (floors 3 to 10).
This means there must be 8 floors below P. Thus, P must live on floor 9.
Step 3: Determine the positions of Y and X.
- Clue: "More than three persons live between P and Y who lives above X."
P lives on floor 9. For there to be more than 3 persons (at least 4 persons) between P and Y, Y must live on floor 4 or lower.
Since floors 2 and 3 are already occupied by S and V, Y must live on floor 4 or floor 1.
Since Y lives above X, Y cannot be on floor 1 (the lowest floor). Therefore, Y lives on floor 4.
Consequently, X must live below Y on the only remaining lower floor, which is floor 1.
Step 4: Determine the position of T.
- Clue: "One person lives between T and Y."
Y is on floor 4. The floor with one person between T and Y can be floor 2 or floor 6.
Since floor 2 is occupied by S, T must live on floor 6.
Step 5: Determine the positions of R and W.
- Clue: "W lives just below R."
This means R and W must occupy two consecutive vacant floors, with R directly above W.
Let's list the currently vacant floors: 10, 8, 7, and 5.
The only consecutive vacant floors are 8 and 7. Thus, R lives on floor 8 and W lives on floor 7.
Step 6: Place the remaining persons, U and Q.
- The remaining vacant floors are 10 and 5, and the remaining persons are U and Q.
- Clue: "U does not live below Q."
This means U must live above Q. Therefore, U lives on floor 10 and Q lives on floor 5.
Final Floor Arrangement:
Floor 10: U
Floor 9: P
Floor 8: R
Floor 7: W
Floor 6: T
Floor 5: Q
Floor 4: Y
Floor 3: V
Floor 2: S
Floor 1: X
Therefore, U lives on the topmost floor (floor 10).
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