When is Manohar's birthday this year? Statement I: It falls between January 13 and January 15, and January 13 is a Wednesday. Statement II: It is not on a Friday.

Introduction / Context:
This data sufficiency question asks you to determine the exact date of Manohar's birthday in January of a particular year. Two statements limit the possible dates and give information about the weekday of certain days. The objective is to decide whether one statement alone, or a combination of both, gives enough information to identify the unique date of his birthday.

Given Data / Assumptions:
- Question: On which date in January does Manohar's birthday fall this year?
- Statement I: It is between January 13 and January 15, and January 13 is a Wednesday.
- Statement II: It is not on a Friday.
- The phrase "between January 13 and January 15" is interpreted in the usual logical puzzle sense as meaning the date is 14 January, which lies strictly between 13 and 15.

Concept / Approach:
The key is to interpret the language of the statements precisely. In many aptitude and data sufficiency problems, when a birthday is said to be "between" two specific dates, it is commonly taken to mean the date that lies strictly in the middle. If that interpretation gives a unique date from statement I alone, the second statement may be redundant. On the other hand, statement II only tells us that the birthday is not on a particular weekday, which is very weak information by itself.

Step-by-Step Solution:
Step 1: Analyze statement I. The birthday is said to be between January 13 and January 15. In the usual integer date sense, the only day that lies strictly between the 13th and 15th is the 14th. Step 2: Therefore, statement I alone tells us that Manohar's birthday is on 14 January. The added information that January 13 is a Wednesday may be intended to hint at the weekday sequence, but it is not necessary for determining the date. Step 3: Hence, statement I alone is sufficient to answer the question. Step 4: Now consider statement II alone. It says only that Manohar's birthday is not on a Friday. Without any information about the possible dates or other weekdays, the birthday could be any date in January that is not a Friday. This leaves many possible dates, so statement II alone is clearly not sufficient. Step 5: Since statement I alone suffices and statement II alone does not, we do not need to combine them to answer the question.

Verification / Alternative check:
Even if we try to use the weekday information given in statement I, with January 13 being a Wednesday, this leads to 14 January being a Thursday and 15 January being a Friday. Combining this with statement II would only rule out Friday (15 January), leaving the 13th or 14th as candidates if we misinterpreted "between" as inclusive. However, the standard wording in such puzzles treats "between 13 and 15" as the single day 14. Under that interpretation, statement II is redundant and statement I alone already identifies 14 January as the birthday.

Why Other Options Are Wrong:
- Option b is wrong because statement II alone does not narrow the birthday down to a specific date at all.
- Option c is incorrect since only statement I alone is sufficient; statement II alone is not.
- Option d is wrong because we do not need both statements; I alone suffices.
- Option e is clearly wrong because the date can be determined from statement I alone.

Common Pitfalls:
Learners sometimes misinterpret "between 13 and 15" to mean on one of 13, 14 or 15, which would make statement I ambiguous. It is important in exam style questions to recognize the conventional usage where "between" two distinct dates refers to the date strictly in the middle. Another mistake is to overvalue statement II and try to combine both statements without first checking the sufficiency of I alone.

Final Answer:
Statement I alone is sufficient to determine that Manohar's birthday is on 14 January, whereas statement II alone is not sufficient. Therefore, the correct data sufficiency choice is option A.