Directions: Read the following information carefully and answer the questions given below:
Ten persons—A, B, C, D, E, F, G, H, I, and J—live on different floors of a 10-storey building, where the ground floor is numbered 1, the floor above it is 2, and so on up to the top floor numbered 10.
B lives on an even-numbered floor below floor 5. Three persons live between B and F, who lives immediately below H. D lives on an even-numbered floor above H. Two persons live between H and C, who lives above D. The number of persons living above C is the same as the number of persons living below A. J lives three floors above F. E lives immediately below I and immediately above G.
Which of the following combinations is incorrect?
Correct Answer :
E – 6th Floor
Solution :
The correct answer is E – 6th Floor.
Step-by-step Logical Reasoning:
Step 1: Determine the positions of B, F, H, D, and C.
1. B lives on an even-numbered floor below floor 5. Therefore, B can live on either floor 2 or floor 4.
2. Three persons live between B and F:
- Case A: If B is on floor 2, then F must be on floor 6.
- Case B: If B is on floor 4, then F must be on floor 8.
3. F lives immediately below H (H = F + 1):
- Case A: H is on floor 7.
- Case B: H is on floor 9.
4. D lives on an even-numbered floor above H, and C lives above D with two persons between H and C:
- In Case B (H = 9), placing two persons above H would exceed floor 10, which is invalid.
- In Case A (H = 7), two persons live between H (floor 7) and C, so C must be on floor 10. Since D lives on an even-numbered floor above H (7) and below C (10), D must be on floor 8.
Step 2: Determine the positions of A and J.
1. The number of persons living above C (floor 10) is 0. Therefore, the number of persons living below A must also be 0, which means A lives on floor 1.
2. J lives three floors above F (floor 6). Thus, J lives on floor 6 + 3 = floor 9.
Step 3: Determine the positions of I, E, and G.
1. The remaining vacant floors are floors 5, 4, and 3.
2. E lives immediately below I and immediately above G. Thus, I is on floor 5, E is on floor 4, and G is on floor 3.
Final Floor Arrangement:
- Floor 10: C
- Floor 9: J
- Floor 8: D
- Floor 7: H
- Floor 6: F
- Floor 5: I
- Floor 4: E
- Floor 3: G
- Floor 2: B
- Floor 1: A
Evaluating the Options:
- C – 10th Floor (Correct combination)
- D – 8th Floor (Correct combination)
- H – 7th Floor (Correct combination)
- B – 2nd Floor (Correct combination)
- E – 6th Floor (Incorrect combination, as E lives on the 4th floor)
Hence, E – 6th Floor is the incorrect combination.
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