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# If p is a positive integer, is 2p + 1 prime?

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Manager
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If p is a positive integer, is 2p + 1 prime? [#permalink]

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05 Jul 2010, 02:32
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63% (01:37) correct 37% (01:26) wrong based on 129 sessions

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If p is a positive integer, is 2p + 1 prime?

(1) p is prime
(2) units digit of p is not prime

[Reveal] Spoiler:
may I try here the prime number 2?
Or this option would be inappropriate?
[Reveal] Spoiler: OA

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Manager
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Re: If p is a positive integer, is 2p + 1 prime? [#permalink]

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05 Jul 2010, 05:39
2
KUDOS
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

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Re: If p is a positive integer, is 2p + 1 prime? [#permalink]

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22 Jul 2010, 00:47
statement 1: counterexample p=7
statement 2: counterexample p=4

statements 1 and 2 cannot go together, so answer is E
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Re: If p is a positive integer, is 2p + 1 prime? [#permalink]

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23 Aug 2016, 23:55
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Re: If p is a positive integer, is 2p + 1 prime? [#permalink]

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10 Jan 2017, 22:38
Statement-1:
Consider p=2, 3, 5, 7, 11. In that case, values of 2p+1 are 5, 7, 11, 15 and 23. Here, 15 is not Prime. Hence we cannot be sure if 2p+1 is prime or not. So, statement 1 alone is not sufficient to answer the question.

Statement-2:
Consider p=14, 16, 18. In this case, values of 2p+1 are 29, 33, 37. Here, 33 is not prime. Hence, we cannot be sure if 2p+1 is prime or not. So, statement 2 alone is not sufficient to answer the question.

Both statements together:
Here, select p=19, 29, 59. Here, the values of 2p+1 are 39, 59, 109. Here, 39 is not prime. Still inconclusive.

So, statement E must be the answer
.

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Re: If p is a positive integer, is 2p + 1 prime? [#permalink]

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11 Jan 2017, 00:28
1
KUDOS
serhio wrote:
If p is a positive integer, is 2p + 1 prime?

(1) p is prime
(2) units digit of p is not prime

[Reveal] Spoiler:
may I try here the prime number 2?
Or this option would be inappropriate?

Given P > 0 and Integer

Question : 2p + 1 = prime

As per statement 1: P is prime: 2,3,5,7 and 11 etc.
So 2x2 + 1 = 5 Prime
2x7 + 1 = 15 Not prime (Insufficient)

As per statement 2: 11,12,14,19 etc

11 x 2 + 1 = 23 prime
19 x 2 + 1 = 39 Not prime (Insufficient)

Combining 1 & 2 we can try 11 and 19

Hence (E)
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Re: If p is a positive integer, is 2p + 1 prime?   [#permalink] 11 Jan 2017, 00:28
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# If p is a positive integer, is 2p + 1 prime?

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