Data Sufficiency — Bus Timetable Question: It is 8:00 p.m. in Dhanpur. When can Hemant get the next bus for Ramnagar? Statements: I. Buses for Ramnagar leave after every 30 minutes, till 10:00 p.m. II. Fifteen minutes ago, one bus left for Ramnagar.

Introduction / Context: This Data Sufficiency item checks understanding of periodic events and whether knowing the phase (i.e., the last departure time) is necessary to determine the next departure time.

Given Data / Assumptions:

• Current time = 8:00 p.m.
• Departures occur every 30 minutes (from Statement I).
• A bus left 15 minutes ago (from Statement II), i.e., at 7:45 p.m.

Concept / Approach: For periodic schedules, frequency alone is not enough unless the timing offset (a recent or reference departure) is known. A known last-departure time lets us add the period to get the next departure.

Step-by-Step Solution:

Verification / Alternative check: Whether or not the service runs until 10:00 p.m. does not affect the immediate next departure at 8:15 p.m., since 8:15 p.m. is before 10:00 p.m.

Why Other Options Are Wrong:

• I alone sufficient: No, phase unknown.
• Either alone sufficient: No, only II works.
• Neither sufficient: Incorrect because II works.
• Both required: Unnecessary; II already suffices.

Common Pitfalls: Assuming default departure times (e.g., exactly on the hour/half-hour) without evidence; overlooking that a single recent departure time fixes the phase immediately.

Final Answer: II alone is sufficient while I alone is not sufficient.