GATE CE 2017 Set 2 — Question 65

To evaluate the statements, we analyze the provided graph which shows the floor number at different time intervals (halts of 1 minute each).Statement i: "The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period."
Looking at the graph, at $t = 28$ minutes, the elevator is at Floor 2. At $t = 29$ minutes, it is at Floor 5. There is no halt at the ground floor (Floor 0) between these two non-ground floor halts. Therefore, the elevator moved directly between two non-ground floors, making statement i incorrect.Statement ii: "The elevator stays on the fourth floor for the longest duration over the one hour period."
We count the number of 1-minute halts for each floor based on the points in the graph:

• Floor 0 (Ground Floor): Approximately 25 halts (e.g., at $t = 1, 4, 5, 9, 11, 15-20, 22, 23, 27, 31, 34, 37, 42, 44, 48, 49, 52, 55, 58, 60$)
• Floor 4: 14 halts (at $t = 6, 7, 8, 24, 25, 26, 35, 36, 45, 46, 47, 53, 59, 60$)

Since the elevator spends significantly more time (25 minutes) on the ground floor than on the fourth floor (14 minutes), statement ii is incorrect.Since both statements are incorrect, the correct option is (D).