Directions: There are six steps that lead from the first to the second floor. No two people can be on the same step Mr. A is two steps below Mr. C Mr. B is a step next to Mr. D Only one step is vacant ( No one standing on that step )Denote the first step by step 1 and second step by step 2 etc. i. B&D can be both on odd-numbered steps in one configuration ii. In a particular configuration A and C must either both an odd numbered steps or both an even-numbered steps iii. A person E can be on a step next to the vacant step.

Statement i claims B and D can both be on odd-numbered steps in one configuration. B and D must be adjacent, so if they're both odd, they'd need to be on consecutive odd steps like 1&3, 3&5, or 5&7 (but 7 doesn't exist). Steps 1 and 3 have step 2 between them, not adjacent, so i is false. Statement ii claims A and C must be both odd or both even. Since A is always 2 below C, they have opposite parity (one odd, one even), so ii is false. Statement iii claims a person E can be on a step next to the vacant step. This is true - E could occupy any step adjacent to the vacant one.