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

E

Five

Show Answer

Correct Answer :

Option A

Four

Four

Solution :

To find the number of persons living between W and S, we can determine the exact floor arrangement of the 10-storey building step-by-step using the given clues.

Step 1: Find the floors of V and S
- V lives on a prime numbered floor but below the 4th floor. The prime floors below 4 are 2 and 3.
- S lives below V but not on the ground floor (floor 1).
- If V lived on floor 2, the only floor below it would be floor 1, which cannot be occupied by S. Therefore, V must live on floor 3, and S must live on floor 2.

Step 2: Find the floor of P
- There are as many persons living above S as below P.
- Since S lives on floor 2, there are 8 floors above S (floors 3 to 10).
- Thus, there must be 8 floors below P, which means P lives on floor 9.

Step 3: Find the floors of Y and X
- More than three persons (at least 4 floors) live between P (floor 9) and Y. This means Y must be on floor 4 or lower.
- We are told that Y lives above X. Since floors 2 and 3 are already occupied by S and V, the only way for Y to live above X is if Y is on floor 4 and X is on floor 1.

Step 4: Find the floor of T
- One person lives between T and Y. Since Y is on floor 4, T must be on floor 6 (as floor 2 is occupied by S).

Step 5: Find the floors of R and W
- W lives just below R, which requires two consecutive vacant floors.
- The currently vacant floors are 10, 8, 7, and 5. The only consecutive vacant floors available are 8 and 7. Thus, R must live on floor 8 and W lives on floor 7.

Step 6: Find the floors of U and Q
- The remaining vacant floors are 10 and 5.
- Since U does not live below Q (meaning U lives above Q), U must live on floor 10 and Q lives 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:
W lives on floor 7 and S lives on floor 2. The persons living between W and S are T, Q, Y, and V (on floors 6, 5, 4, and 3 respectively). Therefore, there are exactly four persons living between W and S.

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