2024 · Q70
A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Is p2 + pq + q2 odd where p, q are integers?
Statement Ip + q is even
Statement IIp q is odd Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsNumber System
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
Statement II (pq odd) forces p, q both odd, so p²+pq+q² = odd+odd+odd = odd — sufficient alone. Statement I (p+q even) allows both-even (sum even) or both-odd (sum odd) — insufficient alone. One statement alone suffices — option A.