What day is the fourteenth of a given month ? I. The last day of the month is…

CONCEPT: In a data-sufficiency problem, a statement is sufficient only if it lets you deduce a UNIQUE answer on its own, without outside assumptions. For day-of-week questions specifically, the weekday cycle repeats every 7 days — so once ANY single date's weekday is fixed, every other date's weekday is fixed too, purely by counting forward or backward in multiples of 7. In contrast, reasoning from a date's position relative to the END of a month (e.g. "the last day") additionally requires knowing the month's total day count, since that determines how far back the target date sits.

APPLICATION:

1. Statement I gives the weekday of the LAST day of the month (Wednesday). To reach the 14th from the last day, you must know the offset — i.e., how many days after the 14th the month ends — which depends on whether the month has 28, 29, 30, or 31 days. Since that total is not given, the offset is unknown, and the 14th's weekday cannot be determined. Statement I alone is NOT sufficient.

2. Statement II gives the weekday of the third Saturday (the 17th). Saturdays recur every 7 days, so the Saturdays in the month are the 3rd, 10th, 17th, and 24th (17 − 7 = 10, 10 − 7 = 3) — entirely independent of the month's length.

3. The 14th is exactly 3 days before the 17th. Counting back from Saturday: Friday (16th), Thursday (15th), Wednesday (14th). So the 14th is a Wednesday, determined uniquely using Statement II alone.

CROSS-CHECK: Counting forward from the 14th as Wednesday — Thursday (15th), Friday (16th), Saturday (17th) — reproduces the given fact that the 17th is a Saturday, confirming the derivation is internally consistent.

RESULT: Statement I alone cannot fix the 14th's weekday (the month length is unknown), while Statement II alone fixes it uniquely via the 7-day cycle. So only Statement II's data is needed to answer the question.