What day of the week is the fourteenth of a given month? Statement I: The last day of the month is a Wednesday. Statement II: The third Saturday of the month falls on the seventeenth.

Introduction / Context:
This is a day of week data sufficiency question. You are asked to determine the weekday of the fourteenth day of a month. Two statements describe the weekday of the last day of the month and the date of the third Saturday. Your goal is to decide whether either statement alone, or both together, provide enough information to determine the weekday of the fourteenth.

Given Data / Assumptions:
- Question: What day of the week is the fourteenth of a given month?
- Statement I: The last day of the month is a Wednesday.
- Statement II: The third Saturday of the month was on the seventeenth.
- No specific month or year is given; only relative day information is provided.

Concept / Approach:
The weekday of any specific date can be determined if we know the weekday of another nearby date together with the difference in days. Statement II relates the seventeenth to a Saturday, which is only three days away from the fourteenth, making it especially powerful. By contrast, knowing only the weekday of the last day of a month does not directly tie to the fourteenth without knowing the total number of days in that particular month.

Step-by-Step Solution:
Step 1: Consider statement I alone. It tells us that the last day of the month is a Wednesday, but we do not even know whether the month has 28, 29, 30, or 31 days. Step 2: Since both the exact length of the month and its starting weekday are unknown, many different configurations of weekdays are consistent with the last day being Wednesday. Therefore, we cannot uniquely determine the weekday of the fourteenth from statement I alone. Statement I is not sufficient. Step 3: Now consider statement II alone. It says that the third Saturday of the month is on the seventeenth. That means that the date 17 falls on a Saturday. Step 4: Working backwards, the sixteenth is a Friday, the fifteenth is a Thursday, and the fourteenth is a Wednesday, because each previous date is one day earlier in the week. Step 5: Therefore, using statement II alone, we can determine that the fourteenth is a Wednesday.

Verification / Alternative check:
We can cross check the logic: if the seventeenth is the third Saturday, earlier Saturdays would be on the third and tenth. The weekly spacing is consistent. Starting from 17 (Saturday), we move backward three days to reach 14 (Wednesday). This calculation does not depend on the total number of days in the month, so the result remains valid regardless of the month length. Thus statement II alone gives a unique weekday for the fourteenth.

Why Other Options Are Wrong:
- Option a is wrong because statement I alone does not let us deduce the weekday of the fourteenth due to the uncertainty about the month length and the starting day.
- Option c is incorrect because it suggests that both statements individually are sufficient, while in fact only statement II is.
- Option d is wrong because we do not need to combine the statements; statement II alone already gives the answer.
- Option e is clearly wrong since at least one statement (II) is sufficient to solve the problem.

Common Pitfalls:
Some students mistakenly try to infer something about the fourteenth from the last day of the month without knowing the length of the month, which leads to multiple possibilities. Another pitfall is overcomplicating the analysis of statement II by trying to construct a full calendar rather than simply counting backwards three days from the seventeenth. Recognizing that dates separated by three days fall on weekdays separated by three positions is the key here.

Final Answer:
Statement II alone is sufficient to determine that the fourteenth is a Wednesday, while statement I alone is not sufficient. Hence, the correct data sufficiency choice is option B.