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16 Sep 2014, 00:17
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16 Sep 2014, 00:17
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Official Solution:
Is \(p^2 \gt q^2\)?
Given that both sides of the inequality are nonnegative, we can safely take the square root of both sides, resulting in the question: is \(|p| > |q|\)? Essentially, the question asks whether \(p\) is farther from zero on the number line than \(q\) is.
(1) \(p \gt 0\).
This doesn't provide sufficient information, as we know nothing about \(q\).
(2) \(q \gt 0\).
Similarly, this doesn't provide sufficient information, as we know nothing about \(p\).
(1)+(2) Knowing that both \(p\) and \(q\) are positive doesn't clarify which one is farther from zero. We are still uncertain about their relative positions on the number line. Not sufficient.
Answer: E
Is \(p^2 \gt q^2\)?
Given that both sides of the inequality are nonnegative, we can safely take the square root of both sides, resulting in the question: is \(|p| > |q|\)? Essentially, the question asks whether \(p\) is farther from zero on the number line than \(q\) is.
(1) \(p \gt 0\).
This doesn't provide sufficient information, as we know nothing about \(q\).
(2) \(q \gt 0\).
Similarly, this doesn't provide sufficient information, as we know nothing about \(p\).
(1)+(2) Knowing that both \(p\) and \(q\) are positive doesn't clarify which one is farther from zero. We are still uncertain about their relative positions on the number line. Not sufficient.
Answer: E
16 Oct 2023, 13:46
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
