Is the integer n odd? A. n2 is odd B. n + 1 is even

In Data Sufficiency questions, a statement is sufficient when it lets you answer the question with a definite yes or a definite no on its own — it does not need to reveal which answer, only make the question decidable. For any integer n, two parity facts govern this question: n is odd if and only if n2 is odd (an odd number squared stays odd, an even number squared stays even), and n is odd if and only if n + 1 is even (consecutive integers always alternate parity).

• Statement A on its own: n2 is odd. Since only an odd base produces an odd square, n2 being odd forces n to be odd. This is a definite “yes” — statement A alone answers the question.

• Statement B on its own: n + 1 is even. Because n + 1 and n always have opposite parity, n + 1 being even forces n to be odd. This is also a definite “yes” — statement B alone answers the question, independently of statement A.

Check with a concrete value: let n = 3. Then n2 = 9, which is odd, matching statement A; and n + 1 = 4, which is even, matching statement B. Both statements independently confirm the same odd value of n, so neither statement depends on the other to reach its conclusion.

Since each statement, evaluated completely on its own, forces a definite answer to the question, the correct classification is that either statement alone is sufficient.