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05 Jul 2010, 02:32
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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.
M14-30
(1) \(p\) is a prime number.
(2) The units digit of \(p\) is not a prime number.
M14-30
may I try here the prime number 2?
Or this option would be inappropriate?
Or this option would be inappropriate?
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05 Jul 2010, 05:39
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Hi,
2 is prime number so you can consider it.
1 - p is prime
p=2, 2p+1=5 is prime
p=3, 2p+1=7 is prime
p=7 2p+1=15 is not prime
So the answer is not sufficient.
2 - The single digit prime numbers are 2,3,5,7
the units digit of p is not prime, hence the units digit of p can be 0,1,4,6,8,9
if p=10, 2p+1=21 is not prime
if p=11, 2p+1=23 is prime
Hence answer 2 is not sufficient.
Now taking 1 and 2 together
prime numbers 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167etc
units digit of p is not prime
possible values of p are:19,29,59,79,89 in other words all prime numbers that are ending with 9.
Assuming p=19, 2p+1=39=3*13 is not prime
Assuming p=29, 2p+1=59 is prime.
Hence taking 1 and 2 together is not sufficient to answer the question.
Ragards,
Jack
2 is prime number so you can consider it.
1 - p is prime
p=2, 2p+1=5 is prime
p=3, 2p+1=7 is prime
p=7 2p+1=15 is not prime
So the answer is not sufficient.
2 - The single digit prime numbers are 2,3,5,7
the units digit of p is not prime, hence the units digit of p can be 0,1,4,6,8,9
if p=10, 2p+1=21 is not prime
if p=11, 2p+1=23 is prime
Hence answer 2 is not sufficient.
Now taking 1 and 2 together
prime numbers 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167etc
units digit of p is not prime
possible values of p are:19,29,59,79,89 in other words all prime numbers that are ending with 9.
Assuming p=19, 2p+1=39=3*13 is not prime
Assuming p=29, 2p+1=59 is prime.
Hence taking 1 and 2 together is not sufficient to answer the question.
Ragards,
Jack
General Discussion
05 May 2023, 11:49
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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
(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
