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If integer p is a factor of 42, is p a prime number?

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Bunuel
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If integer p is a factor of 42, is p a prime number? [#permalink] New post   23 May 2020, 07:36
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If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21


DS21228
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E
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BrentGMATPrepNow
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Re: If integer p is a factor of 42, is p a prime number? [#permalink] New post   23 May 2020, 07:45
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Bunuel wrote:
If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21
DS21228

Given: Integer p is a factor of 42
The positive factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

Target question: Is p a prime number?

Statement 1: p > 6
So, p can equal any of the following values: 7, 14, 21, 42
If n = 7, the answer to the target question is YES, p is prime
If n = 14, the answer to the target question is NO, p is not prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p < 21
So, p can equal any of the following values: 1, 2, 3, 6, 7, 14
If n = 7, the answer to the target question is YES, p is prime
If n = 14, the answer to the target question is NO, p is not prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We can already see that n = 7 and n = 14 satisfy BOTH statements. In other words:
If n = 7, the answer to the target question is YES, p is prime
If n = 14, the answer to the target question is NO, p is not prime
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Brent
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Re: If integer p is a factor of 42, is p a prime number? [#permalink] New post   23 May 2020, 22:52
Bunuel wrote:
If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21

DS21228



Factors of 42: 1,2, 3, 6, 7, 14, 21, 42. Total of 8 factors.

Statement 1: p > 6
The factors > 6 are 7, 14, 21, 42.
p could be any one of the mentioned factors. Thus we cannot determine the value of p with certainty.
=> We cannot say whether p is prime or not.

So Insufficient.


Statement 2: p < 21
Again it could be any factor : 1, 2, 3, 6, 7, 14.
We cannot calculate the specific value of p.
=> We cannot say whether p is prime or not.

So Insufficient.


Statement 1 + Statement 2: 6 < p < 21.
=> the factors that fall in this range are: 7, 14.
One is prime and one is not.
So we cannot say with certainty whether p is prime or not.

So the 2 statements together are also Insufficient.

Answer E.
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If integer p is a factor of 42, is p a prime number? [#permalink] New post   24 May 2020, 00:14
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Bunuel wrote:
If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21


DS21228


P is a factor of 42

Factors of 42 = {1, 2, 3, 6, 7, 12, 14, 21, 42}

Prime factors of 42 = {2, 3, 7}

Question: Is P = one of {2, 3, 7}?

Statement 1: p > 6

i.e. p could be 7 (YES) or 14 (NO) hence

NOT SUFFICIENT

Statement 2: p < 21

i.e. p could be 7 (YES) or 14 (NO) hence

NOT SUFFICIENT

Combining the statements

6 < p < 21

Statement 1: p > 6

i.e. p could be 7 (YES) or 14 (NO) hence

NOT SUFFICIENT

Answer: Option E
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Re: If integer p is a factor of 42, is p a prime number? [#permalink] New post   25 May 2020, 13:30
I marked this question wrong but thanks all for the explanation.

I wrote 42 as 2*3*7 (in multiples of prime number)
I missed the trick that factors could be a combination of prime factors as well (7, 14, 21) and considered only 7 and marked A as correct choice.

But I did consider 7, 6 (3*2), 14 (2*7) while rejecting B (p<21)

Silly mistake :(
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If integer p is a factor of 42, is p a prime number? [#permalink] New post   25 Nov 2020, 14:02
Bunuel wrote:
If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21


DS21228


Factor pairs:
\(1, 42\)
\(2, 21\)
\(6, 7\)
\(14, 3\)

(1) If \(p > 6\), then p can be \(7, 14, 21, 42\). p can be non-prime or prime. INSUFFICIENT.

(2) If \(p < 21\), p can be \(1, 2, 3, 6, 7, 14\). p can be non-prime or prime. INSUFFICIENT.

(1&2) Combined, p can be 7 or 14. INSUFFICIENT.

Answer is E.
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Re: If integer p is a factor of 42, is p a prime number? [#permalink] New post   14 Jun 2023, 15:13
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Re: If integer p is a factor of 42, is p a prime number? [#permalink]
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