Who is the tallest among the brothers A, B, C, D ? Statement 1 : C is shorter…

In Data Sufficiency questions, a statement is sufficient on its own only when the information it gives allows exactly one possible answer to the question asked; if the same statement is equally consistent with two or more different answers, it is insufficient. When a statement fixes a person's rank by saying they are greater or smaller than only one other named person, it locks in an exact position in the ordering - everyone else must fall on the same side of that boundary.

1. From Statement 1, C is shorter than only B, so B is the one person taller than C, and A and D must both be shorter than C too.

2. That places B above C, and C above both A and D, giving the order B > C > {A, D} - no brother is left who could rank above B, so B is confirmed as the tallest using Statement 1 alone.

3. From Statement 2, D is taller than only A, so A is the one person shorter than D, and B and C must both be taller than D.

4. That places B and C above D, giving {B, C} > D > A, but it never compares B with C directly - so Statement 2 alone cannot tell us whether B or C is taller, leaving the top position undecided.

Testing both clues against each other: Statement 1 pins every other brother below the same person (B), so no second name can compete for the top spot - the answer is settled. Statement 2 permits two different rankings of B and C above D, both consistent with the given statement, so it cannot settle the answer by itself.

Since Statement 1 alone fixes a unique tallest brother while Statement 2 alone does not, 'Statement 1 alone is sufficient' is the correct classification.