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

Four

Solution :

The correct option is Four.

Let's determine the floor positions of all ten persons (P, Q, R, S, T, U, V, W, X, Y) step-by-step from floor 1 to 10:
1. Analyze V's position: We are given that V lives on a prime-numbered floor below the 4th floor. The prime numbers below 4 are 2 and 3. Therefore, V lives on either Floor 2 or Floor 3.
2. Analyze S's position: S lives below V but not on the ground floor (Floor 1). Since S must be below V, V cannot live on Floor 2 (as Floor 1 is the only floor below Floor 2, and S cannot live on Floor 1). Thus, V must live on Floor 3, and S must live on Floor 2.
3. Find P's position: We are told that there are as many persons living above S as below P. S lives on Floor 2, which means there are 8 floors above S (Floors 3 to 10). Therefore, there must be 8 floors below P. This means P lives on Floor 9.
4. Locate Y and X: There are more than three persons living between P (Floor 9) and Y. This means there are at least 4 floors between P and Y. Since Y lives below P, Y can live on Floor 4, 3, 2, or 1. However, Floors 3 and 2 are already occupied by V and S. If Y is on Floor 4, there are 4 floors between P and Y (Floors 5, 6, 7, and 8), which satisfies the condition. Since Y lives above X, X must be on a floor below Y. Therefore, Y must be on Floor 4, and X must be on Floor 1 (the only available floor below Floor 4).
5. Locate T: One person lives between T and Y (Floor 4). This means T can be on either Floor 6 or Floor 2. Since Floor 2 is occupied by S, T must live on Floor 6.
6. Locate R and W: W lives just below R. This requires two adjacent vacant floors. The remaining vacant floors are 10, 8, 7, and 5. The only adjacent pair of vacant floors is Floors 8 and 7. Since W lives just below R, R must be on Floor 8 and W must be on Floor 7.
7. Locate U and Q: The remaining vacant floors are Floor 10 and Floor 5. We are given that U does not live below Q (which means U lives above Q). Therefore, U must live on Floor 10 and Q must live on Floor 5.

Summarizing the floor positions from 10 to 1:
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

Now, let's answer the question: How many persons live between W and S?
W lives on Floor 7 and S lives on Floor 2.
The floors between them are Floors 6, 5, 4, and 3 (occupied by T, Q, Y, and V respectively).
Thus, there are exactly four persons living between W and S.

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