Data Sufficiency — Birth Year of Sanjay Question: In which year was Sanjay born? Statements: I. Sanjay is six years older than Gopal. II. Gopal's brother was born in 1982. III. Sanjay's brother is two years younger than Gopal's brother, who was eight years younger than Gopal.

Introduction / Context: This Data Sufficiency question involves ages and birth years. We need to decide which statements together allow us to compute Sanjay’s exact birth year.

Given Data / Assumptions:

• I: Sanjay is 6 years older than Gopal.
• II: Gopal’s brother was born in 1982.
• III: Sanjay’s brother is 2 years younger than Gopal’s brother, who was 8 years younger than Gopal.

Concept / Approach: Use the absolute year from II with the relative age gaps in III to deduce Gopal’s birth year, then apply I to find Sanjay’s year.

Step-by-Step Solution:

Verification / Alternative check: Without III, II alone cannot connect to Gopal; without II, III gives only relative differences but no absolute year. Without I, we only get Gopal’s year, not Sanjay’s. Hence all three are required.

Why Other Options Are Wrong:

• Only I and II: Lacks link between Gopal and his brother’s year.
• Only II and III: Yields Gopal’s year but not Sanjay’s without I.
• Only I and III: All relative, no absolute anchor year.
• None of these: Incorrect since all three together suffice.

Common Pitfalls: Mixing “older” vs “younger” directions; forgetting to anchor relative differences to an absolute birth year; arithmetic sign errors when moving between years.

Final Answer: All I, II and III.