Question : In which year was Rahul born ? Statements :I. Rahul at present is…

Concept: A Data Sufficiency question does not ask for the numeric answer itself — it asks whether the given statement(s) provide enough information to determine that answer uniquely. A statement is sufficient alone only if it fixes the required quantity without needing any outside reference; two statements are jointly sufficient only if, once combined, every quantity they share in common cancels out and leaves the required value fixed.

Application:

1. Let M be the mother's present age.

2. From Statement I: Rahul's present age = M − 25. M is unknown, so Rahul's absolute age — and hence his birth year — cannot be pinned down from Statement I alone.

3. From Statement II: the brother's present age = M − 35, and the brother was born in 1964. This fixes the brother's age relative to the mother, but says nothing about Rahul, so Statement II alone cannot fix Rahul's birth year either.

4. Combine both statements: Rahul's age − Brother's age = (M − 25) − (M − 35) = 10. The unknown mother's age M cancels out, so Rahul is exactly 10 years older than his brother — a fact independent of M or the current year.

5. Since the brother was born in 1964, and Rahul is 10 years older, Rahul was born in 1964 − 10 = 1954.

Cross-check: With brother = 1964 and Rahul = 1954, Rahul's age always exceeds the brother's by exactly 10 years, matching (M − 25) − (M − 35) = 10 for any M. This confirms both statements are needed together — each one alone leaves the mother's age (and therefore Rahul's year) undetermined — so the correct classification is that both statements together are sufficient.