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A, 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. E lives on an even numbered floor but not 6. The sum of floors on which A and E live is 7. F lives immediately above B. The sum of floors on which E and D live is 3. How many people live between A and D?
1
2
3
4
3
Determine E's floor first using even numbers not equal to 6, then use the sum conditions to lock down A, D, and the remaining occupants step by step.
Determine E's floor first using even numbers not equal to 6, then use the sum conditions to lock down A, D, and the remaining occupants step by step.
Step 1: Determine E's Floor
We are given that E lives on an even-numbered floor, but not 6. The possible even floors are 2 and 4. Also, the sum of floors of E and D is 3 (E + D = 3). Since D must be on a valid floor (>= 1), if E were 4, D would be -1 (impossible). Therefore, E must live on Floor 2. Consequently, D lives on Floor 1 (since 2 + 1 = 3).
Step 2: Determine A's Floor
The sum of floors on which A and E live is 7 (A + E = 7). Since E lives on Floor 2, A must live on Floor 5 (7 - 2 = 5).
Step 3: Place B and F, and find the count between A and D
We are told that F lives immediately above B. The remaining floors are 3 and 4, so F lives on Floor 4 and B lives on Floor 3 (with C taking the remaining floor). A is on Floor 5 and D is on Floor 1. The people living between Floor 5 (A) and Floor 1 (D) are on Floors 4 and 3 (2 people).
A: 1 person is incorrect because Floors 4 and 3 both lie between Floor 5 and Floor 1. C: 3 people is incorrect as there are only floors 2, 3, and 4 between 5 and 1, and E is on floor 2. D: 4 people exceeds the total intermediate floors.
B is correct because A lives on floor 5 and D lives on floor
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