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# If p is an integer, is p a prime number?

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Math Expert
Joined: 02 Sep 2009
Posts: 47983
If p is an integer, is p a prime number?  [#permalink]

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10 Dec 2017, 01:25
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Difficulty:

45% (medium)

Question Stats:

55% (01:04) correct 45% (00:32) wrong based on 33 sessions

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If p is an integer, is p a prime number?

(1) p - 2 is a prime number.
(2) p + 2 is a prime number.

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Intern
Joined: 27 Sep 2015
Posts: 6
Re: If p is an integer, is p a prime number?  [#permalink]

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10 Dec 2017, 04:37
(1) Take P=5(prime no ) so p-2=3 (prime no),
Take P=9( non prime no), p-2=7(prime no ) .

Insufficient

(2) Take P=5(prime ) ,p+2=7(prime)
Take P=9(non prime), p+2=11(prime)

Insufficient

Now considering both statement,

We get value of p as 5,9 etc so cannot be determined whether p is prime or not .

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Manager
Joined: 24 Nov 2016
Posts: 152
Re: If p is an integer, is p a prime number?  [#permalink]

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10 Dec 2017, 04:58
Bunuel wrote:
If p is an integer, is p a prime number?

(1) p - 2 is a prime number.
(2) p + 2 is a prime number.

Given: p is an integer, could be (-3,-2,0,1,3...);

(1) p - 2 is a prime number. Primes are positive integers, so p has to be $$≥4$$; If p = 4 (not prime) then p - 2 = 2 (prime), but if p = 5 (prime) then p - 2 = 3 (prime), not suf.
(2) p + 2 is a prime number. If p = 0 (not prime) then p + 2 = 2 (prime), if p = 3 (prime) then p + 2 = 5 (prime), not suf.
(3) p - 2 and p + 2 is a prime. If p = 9 (not prime) then p - 2 = 7 (prime) and p + 2 = 11 (prime), but if p = 5 (prime) then p - 2 = 3 (prime) and p + 2 = 7 (prime), not suf.

Re: If p is an integer, is p a prime number? &nbs [#permalink] 10 Dec 2017, 04:58
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