Question
Download Solution PDFA, 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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