On which date in April is Gautam's birthday? Statement I: Gautam was born exactly 28 years after his mother was born. Statement II: His mother will be 55 years 4 months and 5 days old on August 18 of this year.

Introduction / Context:
This data sufficiency question asks us to determine the exact date in April on which Gautam was born. Instead of giving a direct date, the question supplies information about Gautam's mother and about the age difference between Gautam and his mother. We must see whether this information, individually or together, allows us to pin down a unique date in April for Gautam's birthday.

Given Data / Assumptions:

• We need the date in April of Gautam's birthday.
• Statement I: Gautam was born exactly 28 years after his mother was born.
• Statement II: Gautam's mother will be 55 years 4 months and 5 days old on August 18 of this year.
• Age expressions such as 55 years 4 months and 5 days are interpreted in the usual calendar sense.
• There is no leap year complication in the month day differences for the period considered, other than the normal calendar.

Concept / Approach:
The strategy is:

• Use statement II to work backwards from August 18 to find the exact birth date of the mother.
• Then apply statement I to shift forward by 28 years to get Gautam's birth date, which will have the same day and month but a later year.
• Finally, check whether either statement alone can give the date in April, and whether both together are required.

Because the question asks only for the day in April, the year is not needed for the final answer.

Step-by-Step Solution:
Step 1: From statement II, the mother is 55 years 4 months and 5 days old on August 18 of this year. Step 2: Subtract 5 days from August 18. Counting backwards, 5 days before August 18 is August 13. Step 3: Subtract 4 months from August 13. Four months before August is April. So four months before August 13 is April 13. Step 4: Therefore, the mother's date of birth is April 13, in a year that is 55 years earlier than this year. Step 5: Statement I says that Gautam was born exactly 28 years after his mother. This means that the day and month of his birth are the same as those of his mother, but the year is 28 years later. Step 6: So Gautam is also born on April 13, 28 years after his mother's birth year. Step 7: Since we only need the date in April, we conclude that Gautam's birthday falls on the thirteenth of April. Step 8: Statement I on its own does not give any specific date, since the mother's birthday is not known from that statement alone. Step 9: Statement II on its own gives only the mother's date of birth, not the age difference between mother and son, so it does not directly provide Gautam's birthday.

Verification / Alternative check:
We can verify the calculation of the mother's date of birth by moving forward instead of backward. Start from April 13. Adding 4 months takes us to August 13. Adding 5 days to August 13 gives August 18. Thus 4 months and 5 days after April 13 is August 18. If the mother is 55 years old on that date, then she was born exactly 55 years earlier on April 13. This confirms that our backward calculation is correct. Next, the age gap of 28 years simply shifts the year while keeping the same month and day. Therefore Gautam's birthday must also fall on April 13, which matches our conclusion.

Why Other Options Are Wrong:
Option a is wrong because statement I alone does not tell us when the mother was born, so we cannot find the date in April. Option b is wrong because statement II alone gives only the mother's birth date, not the relationship between her age and Gautam's age. Option c is wrong because neither statement alone is sufficient; both are needed to link the mother's date of birth to Gautam's date of birth. Option e is wrong because, as shown, the combination of both statements leads to a unique date, April 13.

Common Pitfalls:
Students sometimes make errors while working with months and days, especially when counting backwards. A common mistake is to confuse 4 months and 5 days with 4 months and 15 days or to shift the month incorrectly. Another pitfall is to assume that the difference in years alone is enough, without carefully calculating the day and month of the mother's birth. In data sufficiency, one must also resist the temptation to treat a single statement as sufficient just because it looks rich in information. Always make sure that the required target quantity, here the date in April of Gautam's birthday, can be uniquely derived.

Final Answer:
Using both statements together, we find that Gautam's birthday is on the thirteenth of April. Correct option: The data in both statements I and II together are sufficient to answer the question.