A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question

A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: Is (p + q)² − 4pq, where p, q are natural numbers, positive?

Statement I: p < q.

Statement II: p q.

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. (Correct answer)
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 can be answered even without using any of the Statements.

Correct Answer

Option B — The Question can be answered by using either Statement alone.

Detailed Solution & Explanation

The correct answer is The Question can be answered by using either Statement alone..

Key Points

• (p+q)²−4pq = p²+2pq+q²−4pq = p²−2pq+q² = (p−q)².
• This is always ≥ 0. If p ≠ q, it is strictly positive.
• Statement I: p < q → p ≠ q → (p−q)² > 0. Yes, positive.
• Statement II: p > q → p ≠ q → (p−q)² > 0. Yes, positive.
• Either statement alone is sufficient.
• Answer: The Question can be answered by using either Statement alone.