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Determine Sanjay's birth year from the following 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.
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Solution: Step 1: From Statement II, we know that Gopal's brother was born in the year 1982. Step 2: From Statement III, it is stated that Gopal's brother was eight years younger than Gopal. This means Gopal is 8 years older than his brother. Therefore, Gopal's birth year = 1982 - 8 = 1974. Step 3: From Statement I, it is stated that Sanjay is six years older than Gopal. Therefore, Sanjay's birth year = 1974 - 6 = 1968. Step 4: All three statements are necessary and sufficient to determine Sanjay's birth year.
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