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.
On which floor does T live?
Correct Answer :
6th floor
Solution :
The correct answer is 6th floor.
Let us solve the puzzle step-by-step by placing the ten persons (P, Q, R, S, T, U, V, W, X, Y) on the 10 floors (numbered 1 to 10 from bottom to top).
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 lives on either floor 2 or floor 3.
- "S lives below V but not on the ground floor." Since S lives below V and not on floor 1 (ground floor), V cannot be on floor 2 (which would force S to be on floor 1). Thus, V must live on floor 3, and S must live on floor 2.
Let's represent the floors:
Floor 10:
Floor 9:
Floor 8:
Floor 7:
Floor 6:
Floor 5:
Floor 4:
Floor 3: V
Floor 2: S
Floor 1:
Step 2: Place P.
- "There are as many persons live 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 (with floors 1 to 8 below it).
Floor 10:
Floor 9: P
Floor 8:
Floor 7:
Floor 6:
Floor 5:
Floor 4:
Floor 3: V
Floor 2: S
Floor 1:
Step 3: Place Y, X, and T.
- "More than three persons live between P and Y who lives above X." Since P is on floor 9, the number of persons between P and Y must be at least 4. Let's find the possible floors for Y:
If there are 4 persons between P (floor 9) and Y, Y would be on floor 4 (floors 8, 7, 6, 5 are between them).
If there are 5 persons, Y would be on floor 3 (already occupied by V).
If there are 6 persons, Y would be on floor 2 (already occupied by S).
If Y is on floor 1, there are 7 floors between P and Y.
So, Y can be on floor 4 or floor 1. But Y lives above X, so Y cannot be on the bottommost floor (floor 1). Thus, Y must live on floor 4, and X must live on floor 1.
- "One person lives between T and Y." Since Y is on floor 4, T can be on either floor 6 or floor 2. Since floor 2 is occupied by S, T must live on floor 6.
Floor 10:
Floor 9: P
Floor 8:
Floor 7:
Floor 6: T
Floor 5:
Floor 4: Y
Floor 3: V
Floor 2: S
Floor 1: X
Step 4: Place the remaining persons (R, W, U, Q).
- "W lives just below R." The only adjacent vacant floors available are floors 8 and 7. Thus, R must be on floor 8 and W must be on floor 7.
- "U does not live below Q." The remaining vacant floors are floor 10 and floor 5. Since U cannot be below Q, U must live on floor 10 and Q must live on floor 5.
The final arrangement of floors is:
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
Therefore, T lives on the 6th floor.
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