Question: Is p greater than q? Statement-1: p × q is greater than zero. Statement-2: p² is greater than q².…

Question: Is p greater than q? Statement-1: p × q is greater than zero. Statement-2: p² is greater than q². Which one of the following is correct in respect of the above Question and the Statements?
  1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
  2. The Question can be answered by using either Statement alone.
  3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. The Question cannot be answered even by using both the Statements together.

Solution

Statement 1 ($pq > 0$) only tells us p and q have the same sign — not which is larger. Statement 2 ($p^2 > q^2$) only tells us $|p| > |q|$ — not the sign. Even together: p, q same sign and $|p| > |q|$; if both positive, p > q, if both negative, p < q. The question cannot be answered even using both statements together.

Asked in: CSAT 2023

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