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 out who lives on the topmost floor, we can analyze the given conditions step-by-step to determine the floor arrangement of the ten persons (P to Y) on the 10-storey building (numbered 1 to 10 from bottom to top).
Let's list the clues and build the floor grid:
1. V lives on a prime-numbered floor below the 4th floor. The prime numbers below 4 are 2 and 3. Therefore, V lives on either floor 2 or floor 3.
2. S lives below V but not on the ground floor (floor 1).
If V lived on floor 2, the only floor below it is floor 1, which would force S to live on floor 1. But S cannot live on floor 1.
Thus, V must live on floor 3, and S must live on floor 2 (which is below V and not on floor 1).
3. There are as many persons living above S as below P.
Since S is on floor 2, there are 8 floors above S (floors 3 to 10).
This means there must be 8 floors below P, which places P on floor 9.
4. More than three persons live between P (floor 9) and Y. Y lives above X.
Since P is on floor 9, the floors below P are 8, 7, 6, 5, 4, 3, 2, 1.
"More than three persons" means at least 4 floors lie between P and Y.
If there are 4 floors between P (floor 9) and Y: Y can be on floor 4 (with floors 5, 6, 7, 8 between them).
If there are 5 floors between them: Y can be on floor 3 (but floor 3 is occupied by V).
If there are 6 floors between them: Y can be on floor 2 (but floor 2 is occupied by S).
If there are 7 floors between them: Y can be on floor 1.
So Y is either on floor 4 or floor 1.
5. One person lives between T and Y.
If Y is on floor 1, T must be on floor 3 (but floor 3 is occupied by V). Thus, Y cannot be on floor 1.
Therefore, Y must be on floor 4.
Since Y is on floor 4, one person lives between T and Y, which means T can be on floor 6 (floor 2 is occupied by S). So, T is on floor 6.
6. W lives just below R. This means R and W occupy two consecutive floors (R on the upper floor, W on the floor directly below it).
Currently occupied floors:
Floor 9: P
Floor 6: T
Floor 4: Y
Floor 3: V
Floor 2: S
The vacant floors are 10, 8, 7, 5, 1.
Since R and W must be on consecutive floors (R just above W), the only consecutive vacant floors available are floors 8 and 7.
Thus, R lives on floor 8 and W lives on floor 7.
7. Y lives above X.
The remaining vacant floors are 10, 5, and 1.
Since Y is on floor 4 and must live above X, X must live on a floor lower than 4. The only vacant floor below floor 4 is floor 1.
Thus, X lives on floor 1.
8. U does not live below Q (meaning U lives above Q).
The remaining vacant floors are 10 and 5.
Since U lives above Q, U must live on floor 10 and Q must live on floor 5.
Let's write down the final floor arrangement from 10 to 1:
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
From the final arrangement, we see that U lives on the topmost floor (floor 10).
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