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### Hide Tags Joined: 27 Sep 2015
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If p is an integer greater than 1, is p a prime number?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 73% (00:48) correct 27% (00:56) wrong based on 209 sessions

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If p is an integer greater than 1, is p a prime number?

(1) p is a factor of 13
(2) p is a factor of 78

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Re: If p is an integer greater than 1, is p a prime number?  [#permalink]

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RSOHAL wrote:
If p is an integer greater than 1, is p a prime number?

(1) $$p$$ is a factor of 13
(2) $$p$$ is a factor of 78

The question asks whether p is a prime number.

Per statement 1, p is a factor of 13 and as such there are only 2 possible values of p = 1 or 13. But as it is given than p>1, p=13 is the only allowed value. Sufficient

Per statement 2, p is a factor of 78, thus p = 2 or 6 or 13 and you end up getting primes = 2 or 3 but also non primes = 6 or 78. Hence not sufficient.

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Re: If p is an integer greater than 1, is p a prime number?  [#permalink]

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RSOHAL wrote:
If p is an integer greater than 1, is p a prime number?

(1) $$p$$ is a factor of 13
(2) $$p$$ is a factor of 78

Target question: Is p a prime number?

Given: p is an integer greater than 1

Statement 1: p is a factor of 13
The only positive factors of 13 are 1 and 13
Since we're told that p is greater than 1, we can conclude that p MUST equal 13
So, the answer to the target question is YES, p IS a prime number
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: p is a factor of 78
The positive factors of 78 are 1, 2, 3, 6, 13, 26, 39 and 78
Since we're told that p is greater than 1, we can conclude that p COULD equal 2, 3, 6, 13, 26, 39 or 78
If p = 2, then the answer to the target question is YES, p IS a prime number
If p = 6, then the answer to the target question is NO, p is NOT a prime number
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Brent
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Re: If p is an integer greater than 1, is p a prime number?  [#permalink]

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Determine if p is prime.

(1) It is given that p is a factor of 13. Since the only factors of 13 are 1 and 13, and p > 1, it follows that p = 13, and hence p is prime; SUFFICIENT.

(2) It is given that p is a factor of 78. Then p could be prime, since 2 is a factor of 78 and 2 is prime, and p could be composite (i.e., not prime), since 6 is a factor of 78 and 6 is composite; NOT sufficient.

statement 1 alone is sufficient. Re: If p is an integer greater than 1, is p a prime number?   [#permalink] 13 Feb 2020, 02:52
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