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.
Who lives on the topmost floor?
Correct Answer :
U
Solution :
To find out who lives on the topmost floor, we can analyze the clues step-by-step and place each person on their respective floors from 1 to 10.
Let's list the floors from 10 (topmost) down to 1 (bottommost):
10, 9, 8, 7, 6, 5, 4, 3, 2, 1.
Step 1: Determine the positions of V and S.
- "V lives on prime numbered floor but below 4th floor." The prime numbers below 4 are 2 and 3. So, V can live on either floor 2 or floor 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, V cannot live on floor 2 (as there would be no floor left for S except floor 1). 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 live above S as below P."
- S lives on floor 2. The number of floors above S (floors 3 to 10) is 8.
- Therefore, there must be 8 floors below P. This means P lives on floor 9.
Step 3: Determine the position of Y.
- "More than three persons live between P and Y who lives above X."
- "More than three" means at least 4 floors must be between P (floor 9) and Y. Since Y lives below P, Y can live on floor 4, 3, 2, or 1. Let's look at the available floors:
Floors 9 (P), 3 (V), and 2 (S) are already occupied.
- If Y is on floor 4, the number of floors between P (9) and Y (4) is 4 (floors 5, 6, 7, 8), which satisfies "more than three".
- If Y is on floor 1, the number of floors between P (9) and Y (1) is 7, which also satisfies the condition. However, Y lives above X, so Y cannot be on floor 1 because there must be at least one floor below Y for X.
- Thus, Y must live on floor 4. Consequently, X must live below Y, which leaves only floor 1 for X (since floors 2 and 3 are occupied by S and V respectively). So, X lives on floor 1.
Step 4: Determine the position of T.
- "One person lives between T and Y."
- Y is on floor 4. The person T can live on floor 6 or floor 2. Since floor 2 is occupied by S, T must live on floor 6.
Step 5: Determine the positions of W, R, U, and Q.
- Currently, the occupied floors are:
Floor 9: P
Floor 6: T
Floor 4: Y
Floor 3: V
Floor 2: S
Floor 1: X
The vacant floors are 10, 8, 7, and 5.
- "W lives just below R." This means R and W must occupy two consecutive floors (R directly above W). The only vacant consecutive floors available are floors 8 and 7. Thus, R lives on floor 8 and W lives on floor 7.
- This leaves floors 10 and 5 vacant for U and Q.
- "U does not live below Q" means U must live on a higher floor than Q. Therefore, U lives on floor 10 and Q lives on floor 5.
Summarizing the floor arrangement from top to bottom:
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
U lives on the topmost floor (floor 10).
Therefore, the correct option is U.
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