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?
Correct Answer :
Four
Solution :
To find the number of persons living between W and S, we can determine the floor-by-floor arrangement of the ten persons from 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 prime numbers below 4 are 2 and 3.
- S lives below V but not on the ground floor (floor 1).
- If V lived on floor 2, S would have to live on floor 1 (ground floor), which contradicts the condition that S is not on the ground floor. Therefore, V must live on floor 3, and S must live on floor 2.
Step 2: Determine the position 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).
- Therefore, there must be 8 floors below P, which means P lives on floor 9.
Step 3: Determine the positions of Y and T.
- More than three persons live between P (floor 9) and Y, and Y lives above X. This means there must be at least 4 floors between P and Y.
- Let's check the possible floors for Y below floor 9:
• If there are 4 floors between P and Y, Y lives on floor 4.
• If there are 5 floors between P and Y, Y would live on floor 3 (already occupied by V).
• If there are 6 floors between P and Y, Y would live on floor 2 (already occupied by S).
• If Y lives on floor 1, Y cannot be above X because floor 1 is the bottommost floor.
- Therefore, Y must live on floor 4.
- One person lives between T and Y. Since Y is on floor 4, T must be on either floor 6 or floor 2. Since S is on floor 2, T must live on floor 6.
Step 4: Determine the positions of R and W.
- W lives just below R. This requires two consecutive vacant floors.
- The currently occupied floors are 9 (P), 6 (T), 4 (Y), 3 (V), and 2 (S).
- The remaining vacant floors are 10, 8, 7, 5, and 1.
- The only consecutive vacant floors available are 8 and 7. Thus, R lives on floor 8 and W lives on floor 7.
Step 5: Determine the positions of X, U, and Q.
- Y (floor 4) lives above X. The only vacant floor below floor 4 is floor 1, so X must live on floor 1.
- The remaining vacant floors are 10 and 5. Since U does not live below Q, U must live on floor 10 and Q must live on floor 5.
Final 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 the number of persons living between W (floor 7) and S (floor 2).
The floors between floor 7 and floor 2 are floors 6, 5, 4, and 3. The persons living on these floors are T, Q, Y, and V, respectively.
Thus, there are exactly Four persons living between W and S.
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