Eight persons A, B, C, D, E, F, G, and H live on different floors of an eight-floor building, numbered 1 to 8 from bottom to top. One person lives on each floor but not necessarily in the given order.

G lives five floors above C. As many floors are there below C’s floor as above B’s floor. Three floors are there between the floors of B and D. F lives two floors away D. E does not live above H. A doesn’t live on prime numbered floor.

Who among the following lives on floor number 6?

To find the person who lives on floor number 6, we can analyze the clues step-by-step to determine the floor arrangement from bottom to top (numbered 1 to 8).

Step 1: Analyze the positions of G and C
G lives five floors above C. This means:
Floor of G = Floor of C + 5
Since there are 8 floors in total, the possible configurations for C and G are:
Case 1: If C lives on floor 1, then G lives on floor 6.
Case 2: If C lives on floor 2, then G lives on floor 7.
Case 3: If C lives on floor 3, then G lives on floor 8.

Step 2: Apply the relation between C and B
We are given that the number of floors below C's floor is equal to the number of floors above B's floor.
Let us evaluate this for each case:
• For Case 1 (C = 1, G = 6): There are 0 floors below C. Thus, there must be 0 floors above B, which places B on floor 8.
• For Case 2 (C = 2, G = 7): There is 1 floor below C. Thus, there must be 1 floor above B, which places B on floor 7. However, G is already on floor 7 in this case, leading to a conflict. So, Case 2 is eliminated.
• For Case 3 (C = 3, G = 8): There are 2 floors below C. Thus, there must be 2 floors above B, which places B on floor 6.

Step 3: Analyze the position of D
There are three floors between B and D. Let's test our remaining valid cases:
• In Case 1 (B = 8): Counting 3 floors down (7, 6, and 5), D must live on floor 4.
• In Case 3 (B = 6): Counting 3 floors down (5, 4, and 3), D must live on floor 2.

Step 4: Analyze the position of F
F lives two floors away from D (meaning Floor of F = Floor of D ± 2):
• In Case 1 (D = 4): F can live on floor 2 or floor 6. Since G already occupies floor 6, F must live on floor 2.
• In Case 3 (D = 2): F can live on floor 4 (since floor 0 does not exist). Thus, F must live on floor 4.

Step 5: Apply the condition for A
A does not live on a prime-numbered floor (prime floors are 2, 3, 5, and 7):
• In Case 1: The occupied floors are C=1, F=2, D=4, G=6, B=8. The remaining empty floors are 3, 5, and 7. Since all these remaining floors are prime numbers, we cannot place A anywhere. Thus, Case 1 is eliminated.
• In Case 3: The occupied floors are D=2, C=3, F=4, B=6, G=8. The remaining empty floors are 1, 5, and 7. Since floor 1 is not a prime number, A must live on floor 1.

Step 6: Determine E and H
The remaining empty floors are 5 and 7. Since E does not live above H, E must live below H. Therefore, E lives on floor 5 and H lives on floor 7.

Final Floor Arrangement (from floor 8 to 1):
Floor 8: G
Floor 7: H
Floor 6: B
Floor 5: E
Floor 4: F
Floor 3: C
Floor 2: D
Floor 1: A

Therefore, B lives on floor number 6.