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16 Sep 2014, 00:54
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If \(p\) is a positive integer, is \(2p + 1\) a prime number?
(1) \(p\) is a prime number.
(2) The units digit of \(p\) is not a prime number.
(1) \(p\) is a prime number.
(2) The units digit of \(p\) is not a prime number.
16 Sep 2014, 00:54
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Official Solution:
If \(p\) is a positive integer, is \(2p + 1\) a prime number?
(1) \(p\) is a prime number.
If \(p=2\), then \(2p + 1 = 5\), which is prime. However, if \(p=7\), then \(2p + 1 = 15\), which is NOT prime. Not sufficient.
(2) The units digit of \(p\) is not a prime number.
If \(p=6\), then \(2p + 1 = 13\), which is prime. However, if \(p=4\), then \(2p + 1 = 9\), which is NOT prime. Not sufficient.
(1)+(2) If \(p\) is a prime number with a non-prime units digit, it implies that \(p\) is not a single-digit prime and its units digit is either 1 or 9. If \(p=11\), then \(2p + 1 = 23\), which is prime. However, if \(p=19\), then \(2p + 1 = 39\), which is NOT prime. Not sufficient.
Answer: E
If \(p\) is a positive integer, is \(2p + 1\) a prime number?
(1) \(p\) is a prime number.
If \(p=2\), then \(2p + 1 = 5\), which is prime. However, if \(p=7\), then \(2p + 1 = 15\), which is NOT prime. Not sufficient.
(2) The units digit of \(p\) is not a prime number.
If \(p=6\), then \(2p + 1 = 13\), which is prime. However, if \(p=4\), then \(2p + 1 = 9\), which is NOT prime. Not sufficient.
(1)+(2) If \(p\) is a prime number with a non-prime units digit, it implies that \(p\) is not a single-digit prime and its units digit is either 1 or 9. If \(p=11\), then \(2p + 1 = 23\), which is prime. However, if \(p=19\), then \(2p + 1 = 39\), which is NOT prime. Not sufficient.
Answer: E
05 May 2023, 11:48
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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.
