Question
Download Solution PDFA, B, C, D, E and F 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. The product of floors on which D and F live is 10. C lives immediately above E. The sum of floors on which B and D live is 11. How many people live between A and E?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven: A, B, C, D, E and F live on six different floors of the same building, numbered 1 to 6 from bottom to top.
Let's use the given conditions to deduce the floor arrangements:
1. The product of floors on which D and F live is 10.
Possible pairs for (D, F) or (F, D) that multiply to 10 are (2, 5) or (5, 2).
| Case I | Case II | |
|---|---|---|
| Floor No. | Person | Person |
| 6 | ||
| 5 | D | F |
| 4 | ||
| 3 | ||
| 2 | F | D |
| 1 |
The sum of the floors on which B and D live is 11.
- Given D can be on floor 2 or 5:
- If D lives on floor 2, then B + 2 = 11 → B = 9 (case II is not possible as max floor is 6).
- If D lives on floor 5, then B + 5 = 11 → B = 6.
We can definitely say that D lives on floor 5 and B lives on floor 6.
| Case I | |
|---|---|
| Floor No. | Person |
| 6 | B |
| 5 | D |
| 4 | |
| 3 | |
| 2 | F |
| 1 |
2. C lives immediately above E.
This means C and E are on consecutive floors, with C on the higher floor.
| Floor No. | Person |
|---|---|
| 6 | B |
| 5 | D |
| 4 | C |
| 3 | E |
| 2 | F |
| 1 |
The only person left is A, and the only floor left is 1. So, A lives on floor 1.
Final arrangement:
| Floor No. | Person |
|---|---|
| 6 | B |
| 5 | D |
| 4 | C |
| 3 | E |
| 2 | F |
| 1 | A |
Thus, 1 person lives between A and E.
Hence, the correct answer is "Option 2".
Last updated on Jul 19, 2025
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