CSATNumber System & SeriesAlgebra2025

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 – 4 pq, where p, q are natural numbers, positive ? 1. p < q. 2. p > q. Which one of the following is correct in respect of the above Question and the Statements ?

A

The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.

B

The Question can be answered by using either Statement alone.

C

The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

D

The Question can be answered even without using any of the Statements.

Correct Answer: Option B

Explanation

1. **Simplify the Expression**: First, I look at the expression (p + q)² – 4pq. From basic algebra practice [57], I immediately recognize this expands and simplifies: (p² + q² + 2pq)

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