Question Details

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?

Options

A

V

B

T

C

U

D

W

Show Answer

Correct Answer :

Option C

U

Solution :

Correct Answer: U

Let us analyze the given information step-by-step to determine the floor arrangement of all ten persons (P, Q, R, S, T, U, V, W, X, Y) in the 10-storey building, numbered 1 (bottommost) to 10 (topmost).

Step 1: Determine the positions of V and S
- V lives on a prime numbered floor below the 4th floor. The prime numbers below 4 are 2 and 3.
- S lives below V, but not on the ground floor (Floor 1).
- Since S must live below V and cannot be on Floor 1, V cannot be on Floor 2 (otherwise S would have to be on Floor 1). Therefore, V must be on Floor 3.
- Since S lives below V and above Floor 1, S must be on Floor 2.

Step 2: Determine the position of P
- There are as many persons living above S as below P.
- Since S is on Floor 2, there are 8 persons living above S (Floors 3 to 10).
- Therefore, there must be 8 persons living below P, which means P lives on Floor 9.

Step 3: Determine the positions of Y, T, and X
- More than three persons live between P (Floor 9) and Y. Also, Y lives above X.
- If more than 3 persons live between P and Y, the distance between floor 9 and Y's floor must be at least 5 (i.e., Y can be on Floor 4, 3, 2, or 1).
- We already know Floors 2 and 3 are occupied by S and V. Thus, Y can be on Floor 4 or Floor 1.
- There is one person living between T and Y.
- If Y were on Floor 4, then T could be on Floor 6 or Floor 2 (occupied by S). But if Y is on Floor 4 and lives above X, X must be on Floor 1.
- Let us check Y on Floor 4:
  • Y = Floor 4
  • Since Y lives above X, X = Floor 1.
  • One person lives between T and Y ⇒ T = Floor 6 (since Floor 2 is occupied by S).
- Now the occupied floors so far are:
  • Floor 9: P
  • Floor 6: T
  • Floor 4: Y
  • Floor 3: V
  • Floor 2: S
  • Floor 1: X
- Remaining empty floors: 10, 8, 7, 5.
- Remaining persons: Q, R, U, W.

Step 4: Place W, R, Q, and U
- W lives just below R. This means R and W must occupy two consecutive floors (R on top, W directly below).
- Looking at the remaining available floors (10, 8, 7, 5), the only consecutive pair is Floors 8 and 7.
- Therefore, R lives on Floor 8 and W lives on Floor 7.
- Now the remaining empty floors are Floor 10 and Floor 5 for Q and U.
- U does not live below Q, which 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

Hence, U lives on the topmost floor (Floor 10).

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