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

5th floor

E

6th floor

Show Answer

Correct Answer :

Option E

6th floor

6th floor

Solution :

To find the floor on which T lives, we can analyze the given clues step-by-step:

Step 1: Determine the positions of V and S
We are told that V lives on a prime numbered floor below the 4th floor. The prime numbers below 4 are 2 and 3. So, V must live on either the 2nd or 3rd floor.
S lives below V, but not on the ground floor (1st floor). Since S must live on at least the 2nd floor, V cannot live on the 2nd floor.
Therefore, V lives on the 3rd floor and S lives on the 2nd floor.

Step 2: Determine the position of P
There are as many persons living above S as below P.
Since S lives on the 2nd floor, the number of floors above S is:

10 - 2 = 8

This means there must be 8 floors below P. Therefore, P lives on the 9th floor.

Step 3: Determine the positions of Y and X
More than three persons live between P and Y, and Y lives above X.
Since P is on the 9th floor, and more than three persons (at least 4 persons) live between P and Y, Y must live on the 4th floor or lower.
- The 3rd floor is occupied by V.
- The 2nd floor is occupied by S.
- Y must live above X, which means Y cannot live on the 1st floor (ground floor) because X must be below it.
Thus, Y lives on the 4th floor, and X lives on the 1st floor.

Step 4: Find the position of T
One person lives between T and Y. Since Y lives on the 4th floor, T must live on either the 2nd floor or the 6th floor.
Since S is already occupying the 2nd floor, T must live on the 6th floor.

Step 5: Placement of the remaining persons (Verification)
Let's place the remaining persons to verify consistency:
- The remaining vacant floors are the 10th, 8th, 7th, and 5th floors.
- W lives just below R. The only consecutive vacant floors are the 8th and 7th floors. Thus, R lives on the 8th floor and W lives on the 7th floor.
- U does not live below Q (meaning U lives above Q). The remaining vacant floors are the 10th and 5th floors. Therefore, U lives on the 10th floor and Q lives on the 5th floor.

The complete floor arrangement from top to bottom is:
10th floor - U
9th floor - P
8th floor - R
7th floor - W
6th floor - T
5th floor - Q
4th floor - Y
3rd floor - V
2nd floor - S
1st floor - X

Therefore, T lives on the 6th floor.

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