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is p prime number

by Needgmat » Sat Sep 03, 2016 11:27 pm

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

1) p is a factor of 13.

2) p is a factor of 78.

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Please explain why not statement 2 is also suficient
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Sep 04, 2016 2:03 am

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

1) p is a factor of 13.

2) p is a factor of 78.
Statement 1:
Factors of 13:
1*13
Since p must be greater than 1, p=13.
SUFFICIENT.

Statement 2:
Factors of 78:
1*78
2*39
3*26
6*13
It's possible that p=2, in which case p is prime.
It's possible that p=78, in which case p is NOT prime.
INSUFFICIENT.

The correct answer is A.
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by Brent@GMATPrepNow » Wed May 02, 2018 7:55 am

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Needgmat wrote:If p is an integer greater than 1, is p 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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by Jeff@TargetTestPrep » Thu May 03, 2018 3:32 pm

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

1) p is a factor of 13.

2) p is a factor of 78.
We are given that p is an integer greater than 1, and we need to determine whether p is prime.

Statement One Alone:

p is a factor of 13.

13 has only two factors: 1 and 13. Since p is greater than 1, p must be 13, which is prime. (Recall that 1 is NOT a prime number.) Statement one alone is sufficient to answer the question.

Statement Two Alone:

p is a factor of 78.

78 = 2 x 39 = 2 x 3 x 13

Since p could be 39 or 13 (among others), statement two alone is not sufficient to answer the question.

Answer: A

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