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.

On which floor does T live?

Options

A

2nd floor

B

3rd floor

C

4th floor

D

6th floor

Show Answer

Correct Answer :

Option D

6th floor

6th floor

Solution :

To find the floor on which T lives, let us analyze the given information step-by-step for the 10 persons (P, Q, R, S, T, U, V, W, X, Y) living on 10 floors numbered 1 to 10 from bottom to top.

The correct option provided is 6th floor (Option 4).

Step 1: Determine the positions of V, S, and P.
1. "V lives on prime numbered floor but below 4th floor."
The prime numbers below 4 are 2 and 3. So, V can live on either floor 2 or floor 3.
2. "S lives below V but not on the ground floor (floor 1)."
Since S lives below V and S cannot be on floor 1, S must be on floor 2. This implies V must be on floor 3.
So, S = Floor 2 and V = Floor 3.
3. "There are as many persons live above S as below P."
Number of persons living above S (Floor 2) is 10 - 2 = 8.
Therefore, the number of persons living below P must also be 8. This means P lives on floor 9.
So, P = Floor 9.

Step 2: Determine the positions of Y, T, and X.
1. "More than three persons live between P and Y who lives above X."
Since P is on floor 9, more than 3 persons (i.e. at least 4 persons) between P and Y means Y must be on floor 4 or lower.
Since Y lives above X, Y cannot be on floor 1.
Floors 2 and 3 are already occupied by S and V. Thus, Y must live on Floor 4.
Since Y lives above X, X must live on the remaining lower floor, which is Floor 1.
So, Y = Floor 4 and X = Floor 1.
2. "One person lives between T and Y."
Y is on Floor 4. One person between T and Y means T can be on Floor 2 or Floor 6.
Since Floor 2 is occupied by S, T must live on Floor 6.
So, T = Floor 6.

Step 3: Verify remaining positions (W, R, U, Q).
1. "W lives just below R."
The remaining available floors are 5, 7, 8, 10.
Adjacent available floors are 7 and 8, or 5 and 6 (but 6 is occupied by T). Thus, R must be on Floor 8 and W on Floor 7.
2. "U does not live below Q."
The remaining floors are 10 and 5 for U and Q. Since U is not below Q, U must live on Floor 10 and Q 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

Thus, T lives on the 6th floor.

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