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16 Sep 2014, 01:06
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Is \(p^2\) a prime number?
(1) \(p > 1\)
(2) \(\sqrt{p}\) is an integer
(1) \(p > 1\)
(2) \(\sqrt{p}\) is an integer
16 Sep 2014, 01:06
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Official Solution:
Is \(p^2\) a prime number?
Before delving into the statements, note that we are not given that \(p\) is an integer.
(1) \(p > 1\).
If \(p = 2\), the answer is NO. However, if \(p = \sqrt{2}\), the answer is YES. Not sufficient.
(2) \(\sqrt{p}\) is an integer.
If \(\sqrt{p}\) is an integer, then \(p\) must also be an integer. This implies that \(p^2\) cannot be prime, since the square of any integer cannot be a prime. Sufficient.
Answer: B
Is \(p^2\) a prime number?
Before delving into the statements, note that we are not given that \(p\) is an integer.
(1) \(p > 1\).
If \(p = 2\), the answer is NO. However, if \(p = \sqrt{2}\), the answer is YES. Not sufficient.
(2) \(\sqrt{p}\) is an integer.
If \(\sqrt{p}\) is an integer, then \(p\) must also be an integer. This implies that \(p^2\) cannot be prime, since the square of any integer cannot be a prime. Sufficient.
Answer: B
27 Sep 2023, 01:12
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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.
