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

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

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New post 27 Jul 2017, 08:02
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E

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  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? [#permalink]

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

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New post 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.


Is the answer C?

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

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New post 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.


Is the answer C?

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

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

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

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