The question below is followed by three statements numbered I, II and III. Decide which of the statements are sufficient to answer the question.
In which year was Sanjay born?
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 is eight years younger than Gopal.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → All I, II and III are required
In data sufficiency, a set of statements is sufficient only if it leads to one definite answer. Sanjay’s birth year can be found only through Gopal, so we need Gopal’s birth year and the gap between Sanjay and Gopal.
Working from the statements:
II: Gopal’s brother was born in 1982
III: Gopal’s brother is 8 years younger than Gopal, so Gopal was born in 1982 − 8 = 1974
I: Sanjay is 6 years older than Gopal, so Sanjay was born in 1974 − 6 = 1968
Checking each pair:
I and II: no link between Gopal and his brother’s year, so Gopal’s year is unknown: not sufficient
II and III: Gopal’s year (1974) is known, but not Sanjay’s gap from Gopal: not sufficient
I and III: only gaps are known, no actual year: not sufficient
So all three statements are needed.