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 lives three floors above the floor on which A lives?

To find who lives three floors above the floor on which A lives, let us analyze the clues step-by-step and determine the floor arrangement of the eight persons A, B, C, D, E, F, G, and H on floors 1 to 8.

Step 1: Determine the positions of G and C
We are given that G lives five floors above C. This means:
$G-C=5$
Since there are 8 floors, the possible pairs for (C, G) are:
• Case 1: C lives on floor 1, G lives on floor 6
• Case 2: C lives on floor 2, G lives on floor 7
• Case 3: C lives on floor 3, G lives on floor 8

Step 2: Determine the position of B using C
We are given that "As many floors are there below C's floor as above B's floor."
Let us evaluate this for each case:
• Case 1: C is on floor 1. There are 0 floors below C. Thus, there must be 0 floors above B, which means B lives on floor 8.
• Case 2: C is on floor 2. There is 1 floor below C. Thus, there must be 1 floor above B, which means B lives on floor 7. However, G is also on floor 7 in this case, which is a contradiction because only one person lives on each floor. So, Case 2 is eliminated.
• Case 3: C is on floor 3. There are 2 floors below C. Thus, there must be 2 floors above B, which means B lives on floor 6.

Step 3: Analyze Case 1 (C = 1, G = 6, B = 8)
• We are given that three floors are between B and D. Since B is on floor 8, D must be on floor 4.
• F lives two floors away from D. Since D is on floor 4, F could live on floor 6 or floor 2. Since G is already on floor 6, F must be on floor 2.
• This leaves floors 3, 5, and 7 vacant for A, E, and H.
• We are told that "A doesn’t live on a prime numbered floor." However, the vacant floors 3, 5, and 7 are all prime numbers. Thus, Case 1 is eliminated.

Step 4: Analyze Case 3 (C = 3, G = 8, B = 6)
• Three floors are between B (floor 6) and D. This means D must live on floor 2.
• F lives two floors away from D. Since D is on floor 2, F must live on floor 4.
• Currently, we have the following layout:
Floor 8: G
Floor 7: Vacant
Floor 6: B
Floor 5: Vacant
Floor 4: F
Floor 3: C
Floor 2: D
Floor 1: Vacant

• The vacant floors are 1, 5, and 7.
• We are given: "A doesn’t live on a prime numbered floor." The prime numbers among the vacant floors are 5 and 7. Since 1 is not a prime number, A must live on floor 1.
• Now, only floors 5 and 7 are vacant for E and H.
• We are given: "E does not live above H." This means E lives on a lower floor than H. Thus, E lives on floor 5, and H lives on floor 7.

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

Answer to the Question:
We need to find who lives three floors above the floor on which A lives.
Since A lives on floor 1, the floor that is three floors above A is:
$1+3=4$
Looking at our final arrangement, F lives on floor 4.