There are seven persons up on a ladder, A, B, C, D, E, F and G (not in that order). A is further up than E but is lower than C. B is in the middle. G is between A and B. E is between B and F. If F is between E and D, the person on the bottom step of the ladder will be
- AB
- BF
- CDCorrect
- DE
Explanation
Let's determine the positions of the seven persons (1 being the top, 7 being the bottom):
-
"B is in the middle." Since there are 7 persons, the middle position is the 4th. _ _ _ B _ _ _ (Position 4 is B)
-
"A is further up than E but is lower than C." This gives us the order: C > A > E (C is above A, A is above E).
-
"G is between A and B." This means either A > G > B or B > G > A.
- If B > G > A, then B is 4th, G would be 5th, A 6th, and E 7th (from C > A > E). This would be: _ _ _ B G A E. C would be above A, so C could be 1st, 2nd, or 3rd.
- If A > G > B, then C > A > G > B. Since B is 4th, this places C at 1st, A at 2nd, and G at 3rd. C A G B _ _ _ Let's proceed with the second case (C A G B _ _ _) as it seems to fit the higher positions directly. In this case, E must be below B (since C > A > E and A > G > B).
-
"E is between B and F." From C A G B _ _ _, B is 4th. E must be below B. So, B > E > F. This places E at 5th and F at 6th. C A G B E F _
-
"If F is between E and D..." From C A G B E F _, E is 5th and F is 6th. For F to be between E and D, D must be below F. So, E > F > D. This places D at the 7th (bottom) position. The complete order is: C A G B E F D
Let's check the alternative from step 3 (B > G > A): If the order was _ _ _ B G A E (B is 4th, G 5th, A 6th, E 7th). Then "E is between B and F" would require B > E > F or F > E > B. Neither is possible if E is already at the very bottom (7th position). So, this alternative is invalid.
Therefore, the only valid sequence is C A G B E F D.
The person on the bottom step of the ladder (7th position) is D.
The final answer is C

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