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.
How many persons live between G and C?
Correct Answer :
More than three
Solution :
To find the number of persons living between G and C, we can analyze the clues step-by-step to determine the complete floor arrangement of the eight-floor building (numbered 1 to 8 from bottom to top).
Step 1: Determine the positions of G and C
G lives five floors above C. This means if C lives on floor , G lives on floor .
Since there are only 8 floors, the possible values for C and G are:
• Case 1: C lives on floor 1, and G lives on floor 6.
• Case 2: C lives on floor 2, and G lives on floor 7.
• Case 3: C lives on floor 3, and G lives on floor 8.
Step 2: Apply the relation between C and B
We are told: "As many floors are there below C’s floor as above B’s floor."
• In Case 1: C is on floor 1 (0 floors below C). Therefore, B must be on floor 8 (0 floors above B).
• In Case 2: C is on floor 2 (1 floor below C). Therefore, B must be on floor 7 (1 floor above B). However, G is already on floor 7. This creates a conflict, so Case 2 is eliminated.
• In Case 3: C is on floor 3 (2 floors below C). Therefore, B must be on floor 6 (2 floors above B).
Step 3: Analyze Case 3 (C = 3, G = 8, B = 6)
"Three floors are there between the floors of B and D."
Since B is on floor 6, D must be on floor 2 (so that floors 5, 4, and 3 are between them).
"F lives two floors away from D."
Since D is on floor 2, F must be on floor 4 (since floor 0 does not exist).
So far, the arrangement is:
• Floor 8: G
• Floor 7: Empty
• Floor 6: B
• Floor 5: Empty
• Floor 4: F
• Floor 3: C
• Floor 2: D
• Floor 1: Empty
Step 4: Place the remaining persons (A, E, H)
The vacant floors are 1, 5, and 7.
"A doesn't live on prime numbered floor."
Out of the remaining floors (1, 5, and 7), floors 5 and 7 are prime numbers. Therefore, A must live on floor 1 (which is not a prime number).
Now, floors 5 and 7 are left for E and H.
"E does not live above H."
This means E lives below H. Thus, E must be on floor 5 and H must be on floor 7.
Final Complete 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
Conclusion:
The floors between G (floor 8) and C (floor 3) are floors 7, 6, 5, and 4. The persons living on these floors are H, B, E, and F.
Therefore, there are exactly 4 persons living between G and C, which corresponds to More than three.
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