Question: It is 8.00 p.m., when can Hemant get next bus for Ramnagar from…
2025
Question: It is 8.00 p.m., when can Hemant get next bus for Ramnagar from Dhanpur?
Statements:
Buses for Ramnagar leave after every 30 minutes, till 10 p.m.
Fifteen minutes ago, one bus has left for Ramnagar.
- A.
I alone is sufficient while II alone is not sufficient
- B.
II alone is sufficient while I alone is not sufficient
- C.
Either I or II is sufficient
- D.
Neither I nor II is sufficient
- E.
Both I and II are sufficient
Show answer & explanation
Correct answer: E
Concept: A statement (or combination of statements) in a data-sufficiency question is sufficient only when it lets you compute one single, unique answer to the question asked; if any piece needed for that unique computation is missing, it is insufficient.
Application: The question asks for the exact clock time of the next bus.
Statement I alone: gives only the spacing between buses (every 30 minutes, till 10 p.m.) but no reference departure time, so many different actual schedules (e.g. buses at 6:00, 6:30, 7:00... or at 6:10, 6:40, 7:10...) fit it -- insufficient alone.
Statement II alone: gives only one reference time (a bus left 15 minutes before 8:00 p.m., i.e. at 7:45 p.m.) but no spacing, so the next bus could arrive minutes away or much later -- insufficient alone.
Combining both: from Statement II the last bus left at 7:45 p.m.; from Statement I the next one follows 30 minutes later, so the next bus leaves at 7:45 p.m. + 30 minutes = 8:15 p.m. -- a unique time is computable only by using both statements together.
Cross-check: 8:15 p.m. is well before the 10 p.m. cut-off given in Statement I, so the computed time is consistent with the stated schedule window.
Result: Neither statement alone pins down a unique departure time, but the two together do -- so both I and II together are sufficient.