Question Is p greater than q Statement 1 p x q is greater than zero Statement 2 p sup2 is ...........

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Question: Is p greater than q?

Statement-1: p x q is greater than zero.

Statement-2: p² is greater than q². The Which one of the following is correct in respect of the above Question and the Statements?

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Complete-Test, Previous year (2023)

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

The Question can be answered by using either Statement alone.

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

The Question cannot be answered even by using both the Statements together.

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Explanation:

- Statement 1: \(p \times q > 0\) implies both \(p\) and \(q\) are either positive or negative. However, it doesn't provide information about their relative sizes.

- Statement 2: \(p^2 > q^2\) indicates that the absolute value of \(p\) is greater than the absolute value of \(q\). But it doesn't clarify which number is actually greater because both could be negative or positive.

- Option 1: Neither statement alone provides a definitive answer about whether \(p\) is greater than \(q\).

- Option 2: Since neither statement alone works, this option is not correct.

- Option 3: Even combined, the statements don't conclusively ensure \(p > q\), as signs of \(p\) and \(q\) could be the same or different.

- Option 4: Both statements together still leave uncertainty about the exact relationship between \(p\) and \(q\).