A, F, J, K, P and Q live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6. F lives on an even numbered floor but not on floor number 4. Only two people live between F and K. J lives on an odd numbered floor but not on the lowermost floor. Only two people live between J and Q. A lives immediately below J. How many people live between P and A?

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  1. Four
  2. Two
  3. Three
  4. One

Answer (Detailed Solution Below)

Option 2 : Two
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Given:

A, F, J, K, P and Q live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

F lives on an even numbered floor but not on floor number 4. This means F can be on floor 2 or floor 6.

Case 1: F lives on floor 2.

Floor Person
6  
5  
4  
3  
2 F
1  

Only two people live between F (floor 2) and K. This means K lives on floor 5.

Floor Person
6  
5 K
4  
3  
2 F
1  

J lives on an odd numbered floor but not on the lowermost floor. This means J can live on floor 3 or floor 5. Since floor 5 is occupied by K, J must live on floor 3.

Floor Person
6  
5 K
4  
3 J
2 F
1  

Only two people live between J (floor 3) and Q. This means Q lives on floor 6.

Floor Person
6 Q
5 K
4  
3 J
2 F
1  

A lives immediately below J. This means A lives on floor 2. But F also lives on floor 2. This case is not possible.

Case 2: F lives on floor 6.

Floor Person
6 F
5  
4  
3  
2  
1  

Only two people live between F (floor 6) and K. This means K lives on floor 3.

Floor Person
6 F
5  
4  
3 K
2  
1  

J lives on an odd numbered floor but not on the lowermost floor. This means J can live on floor 3 or floor 5. Since floor 3 is occupied by K, J must live on floor 5.

Floor Person
6 F
5 J
4  
3 K
2  
1  

Only two people live between J (floor 5) and Q. This means Q lives on floor 2.

Floor Person
6 F
5 J
4  
3 K
2 Q
1  

A lives immediately below J. This means A lives on floor 4.

Floor Person
6 F
5 J
4 A
3 K
2 Q
1  

The only remaining person is P, who must live on the only remaining floor, which is 1.

Floor Person
6 F
5 J
4 A
3 K
2 Q
1 P

Thus, there are two people living between P and A (Q and K).

Hence, the correct answer is 2.

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