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# If N is a positive odd integer, is N prime?

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Board of Directors
Joined: 01 Sep 2010
Posts: 3416
If N is a positive odd integer, is N prime? [#permalink]

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27 Jul 2017, 08:02
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Difficulty:

85% (hard)

Question Stats:

51% (01:24) correct 49% (01:31) wrong based on 279 sessions

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If N is a positive odd integer, is N prime?

(1) $$N = 2^k+ 1$$ for some positive integer k.

(2) N + 2 and N + 4 are both prime.

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Math Expert
Joined: 02 Aug 2009
Posts: 5887
If N is a positive odd integer, is N prime? [#permalink]

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27 Jul 2017, 09:00
2
carcass wrote:
If N is a positive odd integer, is N prime?

(1) $$N = 2^k+ 1$$ for some positive integer k.

(2) N + 2 and N + 4 are both prime.

hi...

lets see the statements..

(1) $$N = 2^k+ 1$$ for some positive integer k.
if k = 2, N = $$2^2+1=5$$.. YES
if k= 3, N=$$2^3+1=9$$... No
Insuff

(2) N + 2 and N + 4 are both prime
if N+2 and N+4 are prime, ONE of N or N+2 or N+4 will surely be MULTIPLE of 3..
so N can be prime only when N=3, otherwise always NO
Insuff

combined
Nothing new

E
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: If N is a positive odd integer, is N prime? [#permalink]

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27 Jul 2017, 09:08
1
carcass wrote:
If N is a positive odd integer, is N prime?

(1) $$N = 2^k+ 1$$ for some positive integer k.

(2) N + 2 and N + 4 are both prime.

from 1, k=1,2 satisfy, but k=3 doesn't.
insuff

from 2, N=1, 3 satisfy, but 1 is neither prime nor composite.
insuff

together, N =3 satisfies both the criteria.
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Joined: 21 May 2013
Posts: 646
If N is a positive odd integer, is N prime? [#permalink]

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27 Jul 2017, 09:12
rekhabishop wrote:
carcass wrote:
If N is a positive odd integer, is N prime?

(1) $$N = 2^k+ 1$$ for some positive integer k.

(2) N + 2 and N + 4 are both prime.

from 1, k=1,2 satisfy, but k=3 doesn't.
insuff

from 2, N=1, 3 satisfy, but 1 is neither prime nor composite.
insuff

together, N =3 satisfies both the criteria.

Answer will be E , N can be 3 or 9.
Intern
Joined: 22 Mar 2017
Posts: 28
GMAT 1: 680 Q48 V35
If N is a positive odd integer, is N prime? [#permalink]

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08 Jan 2018, 07:18
1
If N is a positive odd integer, is N prime?

(1) N=2^k+1N for some positive integer k.

N can be 3, 5, or 9 using values of k = 1, 2 and 3 respectively

INSUFF

(2) N + 2 and N + 4 are both prime.

If N = 3 then N + 2 = 5 and N + 4 = 7 COMPLIES (we pick the first prime of the examples used for S1).
If N = 9 then N + 2 = 11 and N + 4 = 13 COMPLIES (we pick the first non-prime of the examples used for S1).

INSUFF

(1)(2)

Same examples fulfill both Ss (in this case the prime 3 and the non-prime 9).

INSUFF

AC: E

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Joined: 02 Aug 2009
Posts: 5887
Re: If N is a positive odd integer, is N prime? [#permalink]

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15 Jun 2018, 22:45
chetan2u wrote:
carcass wrote:
If N is a positive odd integer, is N prime?

(1) $$N = 2^k+ 1$$ for some positive integer k.

(2) N + 2 and N + 4 are both prime.

hi...

lets see the statements..

(1) $$N = 2^k+ 1$$ for some positive integer k.
if k = 2, N = $$2^2+1=5$$.. YES
if k= 3, N=$$2^3+1=9$$... No
Insuff

(2) N + 2 and N + 4 are both prime
if N+2 and N+4 are prime, ONE of N or N+2 or N+4 will surely be MULTIPLE of 3..
so N can be prime only when N=3, otherwise always NO
Insuff

combined
Nothing new

E

Responding to a PM ...
Why should one of n, n+2 or n+4 be a multiple of 3....
If n is odd, all three will be odd....
1,3,5 or 3,5,7.... In these 3 is multiple of 3
Next three are 5,7,9..., So here 3 has moved out of set but 9 has come in
Say n is even
2,4,6 or 4,6,8 or 6,8,10.... Here 6 is present
Next would be 8,10,12.... So 6 has moved out but 12 has come in...

The reason for this is the multiple of 3 comes after 3..
Similarly if you are looking for say n,n+2,.....n+12 these are 7 terms and any one of them would surely be multiple of all odd prime numbers till 7... 3,5,7
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: If N is a positive odd integer, is N prime?   [#permalink] 15 Jun 2018, 22:45
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