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

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Manager
Joined: 04 Feb 2009
Posts: 245
Location: Ukraine
Schools: Ross 2013
WE 1: Pharmaceutical industry 5 years, C level
Followers: 4

Kudos [?]: 16 [0], given: 20

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

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05 Jul 2010, 02:32
00:00

Difficulty:

85% (hard)

Question Stats:

48% (02:55) correct 52% (01:09) wrong based on 21 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

may I try here the prime number 2?
Or this option would be inappropriate?
[Reveal] Spoiler: OA
Manager
Joined: 16 Apr 2010
Posts: 221
Followers: 4

Kudos [?]: 108 [1] , given: 12

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05 Jul 2010, 05:39
1
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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Joined: 03 Mar 2010
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Kudos [?]: 14 [0], given: 1

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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: m14 q 30   [#permalink] 22 Jul 2010, 00:47
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