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.

Four of the following five are alike in a certain way and hence form a group. Which of the following does not belong to that group?

Options

A

V

B

T

C

S

D

W

Show Answer

Correct Answer :

Option B

T

T

Solution :

To find the odd one out, let us first determine the floor on which each of the ten persons lives by analyzing the given clues step-by-step.

Step 1: Determine the positions of V and S.
- V lives on a prime-numbered floor below the 4th floor. The floors below the 4th floor are 1, 2, and 3. The prime numbers in this range are 2 and 3.
- S lives below V, but S does not live on the ground floor (floor 1).
- If V lived on floor 2, then S would have to live on floor 1, which contradicts the condition that S is not on floor 1. Therefore, V must live on floor 3.
- Since S lives below V (floor 3) but not on floor 1, S must live on floor 2.

Step 2: Find the position of P.
- There are as many persons living above S as below P.
- Since S lives on floor 2, the number of floors above S is:
10 - 2 = 8
- Thus, there must be 8 floors below P, which means P lives on floor 9.

Step 3: Find the positions of Y and X.
- More than three persons live between P (floor 9) and Y, and Y lives above X. This means there are at least 4 floors between P and Y.
- Counting down from floor 9 with at least 4 floors in between (floors 8, 7, 6, 5), Y must be on floor 4 or lower.
- Since floors 3 and 2 are occupied by V and S, Y could occupy floor 4 or floor 1.
- However, since Y lives above X, Y cannot live on floor 1. Therefore, Y lives on floor 4, and X lives on floor 1.

Step 4: Find the position of T.
- One person lives between T and Y (floor 4).
- This means T can be on floor 6 or floor 2. Since S is already on floor 2, T must live on floor 6.

Step 5: Find the positions of R and W.
- W lives just below R. This requires two adjacent vacant floors.
- The currently vacant floors are 5, 7, 8, and 10. The only consecutive vacant floors are 7 and 8.
- Therefore, R lives on floor 8 and W lives on floor 7.

Step 6: Find the positions of U and Q.
- The remaining vacant floors are 5 and 10.
- Since U does not live below Q, U must live on a floor above Q. Therefore, U lives on floor 10 and Q lives on floor 5.

Let us summarize the final floor arrangement from top to bottom:

Floor Number Person
10U
9P
8R
7W
6T
5Q
4Y
3V
2S
1X


Step 7: Find the group logic.
Let us look at the floor numbers of the given options:
- V lives on floor 3 (which is a prime number).
- S lives on floor 2 (which is a prime number).
- W lives on floor 7 (which is a prime number).
- T lives on floor 6 (which is an even composite number, not a prime number).

Since V, S, and W all live on prime-numbered floors, they form a group. T does not live on a prime-numbered floor and therefore does not belong to the group.

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