QUESTION

CSAT

Easy

Maths

Prelims 2025

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)24pq(p + q)^2 - 4pq, where pp, qq are natural numbers, positive? Statement I: p<qp < q. Statement II: p>qp > q.

Which one of the following is correct in respect of the above Question and the Statements?

Select an option to attempt

Explanation

Compute: (p+q)24pq=p2+q2+2pq4pq=p2+q22pq=(pq)2(p + q)^2 - 4pq = p^2 + q^2 + 2pq - 4pq = p^2 + q^2 - 2pq = (p - q)^2.

Since squares are non-negative:

  • If p=q(pq)2=0p = q \Rightarrow (p - q)^2 = 0 (not positive).
  • If $p

eq q \Rightarrow (p - q)^2 > 0$ (positive).

Statement I: $p < q \Rightarrow p

eq q \Rightarrowexpressionispositive.StatementII:expression is positive. Statement II:p > q \Rightarrow p

eq q \Rightarrow$ expression is positive.

Either statement alone suffices to answer “Yes”. Therefore, option B is correct.

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