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A building has seven floors numbered one...

A building has seven floors numbered one to seven , in such a way that the ground floor is numbered one, the floor above it , number two and so on such that the top most floor is numbered seven . One out of seven people , P,Q,R,S,T, U and V lives on each floor. P lives on fourth floor. T lives on the floor immmediately below U's floor. U does not live on second or the seventh floor. R lives on third floor. Q does not live on a floor immediately above or below R's floor. S does not live on the topmost floor. V does not live on any floor below T's floor. Who lives on the top most floor?

A

Q

B

V

C

T

D

U

Text Solution

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The correct Answer is:
To solve the problem step by step, we will analyze the information given and fill in the positions of each person on the respective floors. ### Step 1: List the Floors We have a building with 7 floors, numbered from 1 to 7: - Floor 1 - Floor 2 - Floor 3 - Floor 4 - Floor 5 - Floor 6 - Floor 7 ### Step 2: Place Fixed Positions From the information given: 1. **P lives on the 4th floor.** - So we place P on Floor 4. 2. **R lives on the 3rd floor.** - So we place R on Floor 3. Now our arrangement looks like this: - Floor 1: ? - Floor 2: ? - Floor 3: R - Floor 4: P - Floor 5: ? - Floor 6: ? - Floor 7: ? ### Step 3: Analyze U and T 3. **T lives on the floor immediately below U's floor.** 4. **U does not live on the 2nd or the 7th floor.** - This means U can only live on the 3rd, 5th, or 6th floors. However, since R is on the 3rd floor, U can only be on the 5th or 6th floor. 5. Since T lives immediately below U, if U is on the 5th floor, T must be on the 4th floor, which is not possible since P is already there. Therefore, U must be on the 6th floor, and T must be on the 5th floor. Now our arrangement looks like this: - Floor 1: ? - Floor 2: ? - Floor 3: R - Floor 4: P - Floor 5: T - Floor 6: U - Floor 7: ? ### Step 4: Place Q and S 6. **Q does not live on a floor immediately above or below R's floor.** - Since R is on the 3rd floor, Q cannot be on the 2nd or 4th floors. Therefore, Q must be on the 1st or 7th floor. 7. **S does not live on the topmost floor.** - This means S cannot be on the 7th floor. Therefore, S must be on the 2nd floor. Now our arrangement looks like this: - Floor 1: Q - Floor 2: S - Floor 3: R - Floor 4: P - Floor 5: T - Floor 6: U - Floor 7: ? ### Step 5: Place V 8. **V does not live on any floor below T's floor.** - Since T is on the 5th floor, V must be on the 7th floor. Now our final arrangement looks like this: - Floor 1: Q - Floor 2: S - Floor 3: R - Floor 4: P - Floor 5: T - Floor 6: U - Floor 7: V ### Conclusion The person who lives on the topmost floor (7th floor) is **V**.

To solve the problem step by step, we will analyze the information given and fill in the positions of each person on the respective floors. ### Step 1: List the Floors We have a building with 7 floors, numbered from 1 to 7: - Floor 1 - Floor 2 - Floor 3 - Floor 4 ...
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