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# The positive integer k has exactly two positive prime factors, 3 and 7

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Joined: 01 Nov 2018
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The positive integer k has exactly two positive prime factors, 3 and 7  [#permalink]

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20 Feb 2019, 17:17
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P.S - sorry if I failed to find this using the search tool. I looked into the existing DS database; but could not find this question...
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The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of k ?

(1) 3^{2} is a factor of K.
(2) 7^{2} is not a factor of K.

Need help with this question. The answer to this is option # D; however I am not able to understand how....

Here is my analysis -

6 total factors including, 1, 3, 7, and k. So, let's call the the missing two factors as x and y.

(1) - indicates that 3^2 is a factor - that means there is one more three in the factor list - so lets say x = 3. That leaves y unknown. it could be 3 or 7. Nobody said 3^3 is not a factor.
(2) - indicates that 7^2 is not a factor - this does not mean 7^3 is also not a factor. Hence x and y could be both = 3 or both = 7.

So, in this way, the answer should be C - Together we can say that both the other missing factors are 3 which would suffice conditions 1 and 2.

Thank you!
Intern
Joined: 01 Nov 2018
Posts: 6
Re: The positive integer k has exactly two positive prime factors, 3 and 7  [#permalink]

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20 Feb 2019, 17:32
I found the solution below in the similar question thread and I see my mistake. I confused prime factors with actual factors!

Thanks to Bunnel and everyone who contributed to that thread!
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Math Expert
Joined: 02 Sep 2009
Posts: 53698
Re: The positive integer k has exactly two positive prime factors, 3 and 7  [#permalink]

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20 Feb 2019, 22:03
1
rshah13 wrote:
P.S - sorry if I failed to find this using the search tool. I looked into the existing DS database; but could not find this question...
________________________________________________

The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of k ?

(1) 3^{2} is a factor of K.
(2) 7^{2} is not a factor of K.

Need help with this question. The answer to this is option # D; however I am not able to understand how....

Here is my analysis -

6 total factors including, 1, 3, 7, and k. So, let's call the the missing two factors as x and y.

(1) - indicates that 3^2 is a factor - that means there is one more three in the factor list - so lets say x = 3. That leaves y unknown. it could be 3 or 7. Nobody said 3^3 is not a factor.
(2) - indicates that 7^2 is not a factor - this does not mean 7^3 is also not a factor. Hence x and y could be both = 3 or both = 7.

So, in this way, the answer should be C - Together we can say that both the other missing factors are 3 which would suffice conditions 1 and 2.

Thank you!

Discussed here: https://gmatclub.com/forum/the-positive ... fl=similar
_________________
Re: The positive integer k has exactly two positive prime factors, 3 and 7   [#permalink] 20 Feb 2019, 22:03
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