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

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

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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.

A is the correct answer.
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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

Answer: A

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Brent
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Re: If p is an integer greater than 1, is p a prime number?   [#permalink] 02 May 2018, 09:00
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