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.

How many persons live between W and S?

Options

A

Four

B

Two

C

Three

D

Six

Show Answer

Correct Answer :

Option A

Four

Solution :

The correct option is Four.

Step-by-Step Explanation and Floor Arrangement:

Let us step-by-step determine the floor positions of all 10 persons (P, Q, R, S, T, U, V, W, X, Y) from Floor 10 (topmost) to Floor 1 (bottommost):

1. Determine the positions of V and S:
- "V lives on a prime numbered floor but below 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, S must live on Floor 2, which means V must live on Floor 3.
- Thus, S is on Floor 2 and V is on Floor 3.

2. Determine the position of P:
- "There are as many persons live 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 places P on Floor 9.

3. Determine the positions of Y, T, and X:
- "More than three persons live between P and Y who lives above X."
- Since P is on Floor 9, Y must be at least 4 floors below P (i.e., Floor 4 or lower).
- Floors 1, 2, and 3 are candidate floors, but S is on Floor 2 and V is on Floor 3.
- Also, Y lives above X, so Y cannot be on Floor 1 (since X would have to be below Y).
- Thus, Y must be on Floor 4, and X must be on Floor 1.
- So, Y is on Floor 4 and X is on Floor 1.
- "One person lives between T and Y." Since Y is on Floor 4 and Floor 2 is occupied by S, T must live above Y, which places T on Floor 6.

4. Determine the positions of R, W, U, and Q:
- "W lives just below R." The remaining available contiguous vacant floors are Floor 8 and Floor 7.
- So, R is on Floor 8 and W is on Floor 7.
- "U does not live below Q", which means U lives above Q.
- The remaining empty floors are Floor 10 and Floor 5.
- Therefore, U is on Floor 10 and Q is 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

Conclusion:
We need to find how many persons live between W (Floor 7) and S (Floor 2).
The persons living between W and S are on Floors 6, 5, 4, and 3 (T, Q, Y, V).
Therefore, exactly 4 persons live between W and S.

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