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

Question

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

ENGRTOMBA2018 · Answer

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.

BrentGMATPrepNow · Answer

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

Cheers,
Brent

thouhid · Answer

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.

The correct answer is A;
statement 1 alone is sufficient.

testerchoice · Answer

How did you conclude that P could not be 26? or 39?... (any factor of 13)?

Bunuel · Answer

Integer a is a factor of an integer b means that b/a = integer.
Integer a is a multiple of an integer b means that a/b = integer.

Hence, 26 and 39 are not the factors of 13, they are multiples of 13. 13, being a prime number, has only two positive factors, 1 and 13 itself.

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

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