A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option.<br><br>Question: Is p^2+pq+q^2 odd where p, q are integers?<br><br>Statement-I: p+q is even<br><br>Statement-II: pq is odd<br><br>Which one of the following is correct in respect of the above Question and the Statements ?

  1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone ✓
  2. B. The Question can be answered by using either Statement alone
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D. The Question cannot be answered even by using both the Statements together

Correct Answer: A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

Explanation

Statement II says pq is odd, which means both p and q are odd integers. Their squares are also odd. The sum of three odd numbers (p^2 + pq + q^2) is always odd. Thus, Statement II alone provides a definitive "Yes". Statement I (p+q is even) means both are even or both are odd, which gives ambiguous results.

Related questions on Arithmetic

Practice more CDS Elementary Mathematics questions