In which year was Rahul born? Statement I: At present Rahul is 25 years younger than his mother. Statement II: Rahul's brother, who was born in 1964, is 35 years younger than his mother.

Introduction / Context:
This data sufficiency question concerns ages and years of birth. The goal is to determine the exact year in which Rahul was born. Two statements give information about age differences between Rahul, his brother, and their mother, including a known year of birth for the brother. You must decide whether either statement alone, or both together, are enough to determine Rahul's birth year.

Given Data / Assumptions:
- Question: In which year was Rahul born?
- Statement I: Rahul is at present 25 years younger than his mother.
- Statement II: Rahul's brother was born in 1964 and is 35 years younger than his mother.
- Age differences (gaps) between family members remain constant over time.
- Current year is not explicitly given; we only use relative age differences and the brother's birth year.

Concept / Approach:
We can interpret the information in terms of year of birth. If someone is k years younger than another person, then the younger person's birth year equals the older person's birth year plus k. Statement II gives us the mother's birth year directly because we know the brother's birth year and how much younger he is than his mother. Then we can use this to work out Rahul's birth year if we also know Rahul's age gap with his mother from statement I.

Step-by-Step Solution:
Step 1: Analyze statement I alone. It says Rahul is 25 years younger than his mother. This gives only the age difference and does not reveal any specific calendar year. Without knowing either the current year or the year of birth of the mother, we cannot determine Rahul's birth year. So statement I alone is not sufficient. Step 2: Analyze statement II alone. It says Rahul's brother was born in 1964 and is 35 years younger than his mother. Therefore, mother's birth year = 1964 - 35 = 1929. Step 3: Statement II alone gives us the mother's birth year but does not say how much younger Rahul is than his mother. Without that gap, we cannot compute Rahul's birth year. So statement II alone is also not sufficient. Step 4: Combine both statements. From statement II, mother's birth year is 1929. From statement I, Rahul is 25 years younger than his mother, so Rahul's birth year = 1929 + 25 = 1954. Step 5: With both age gaps and one known birth year, we can now determine a unique birth year for Rahul.

Verification / Alternative check:
We can verify the consistency of the numbers. If the mother was born in 1929, then the brother born in 1964 is indeed 35 years younger (1964 - 1929 = 35). Rahul, being 25 years younger than the mother, must be born in 1929 + 25 = 1954, and the gap between the brother and Rahul is 10 years, which is plausible. There is no contradiction, and the data give a unique year of birth.

Why Other Options Are Wrong:
- Option a is wrong because statement I alone does not yield any year, only a difference in ages.
- Option b is wrong because statement II alone only tells us the mother's birth year but nothing specific about Rahul's gap.
- Option c is incorrect because neither statement alone is sufficient; they must be used together.
- Option e is wrong because, when combined, the two statements clearly allow us to calculate Rahul's birth year, so the data are sufficient.

Common Pitfalls:
A typical error is to misread the phrase "years younger" and try to subtract instead of adding when finding a younger person's birth year. Another pitfall is to assume that knowing one child's year of birth automatically gives the other's year, even when the age difference between the two children is not specified. In data sufficiency, you must track exactly which differences are known and only combine them when logically justified.

Final Answer:
Both statements I and II together are necessary to find that Rahul was born in 1954, so the correct data sufficiency choice is option D.