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Positive Interger

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Positive Interger

by seamaster1 » Sat Apr 27, 2013 5:06 pm
Positive integer k has exactly 2 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?
a. 32 is a factor of k
b. 72 is not a factor of k
Someone please explain the way to solve this kind of question.
Thanks in advance.[/spoiler]
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Source: — Data Sufficiency |
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by gaurav_gaur » Sat Apr 27, 2013 6:37 pm
Hi Seamaster,
The question does not seems correct to me. If a positive integer k is a factor of 32 then it should be having 3 positive prime factors i.e. 2,3 and 7.
Secondly if 32 is a factor of k then least number that satisfy the criteria is 672 which has more than 6 factors.
Can anyone please let me know if I am missing anything here.

Cheers,
GG
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by Anju@Gurome » Sat Apr 27, 2013 10:17 pm
gaurav_gaur wrote:Can anyone please let me know if I am missing anything here.
Your analysis is flawless as per the problem posted.

However, I think the actual problem is as follows...
seamaster1 wrote:Positive integer k has exactly 2 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?

a. 3² is a factor of k
b. 7² is not a factor of k
As the only prime factors of k are 3 and 7, the prime factorization of k will be of the form (2ᵃ)*(3ᵇ), where a and b are some positive integers.
So, number of distinct positive factors of k will be (a + 1)*(b + 1)

If you ask why, refer to the post I made here >> How to find number of factors?

So, (a + 1)(b + 1) = 6
As, a and b are positive integers, only possible values of a and b are : {a = 1, b = 2} or {a = 2, b = 1}

Statement 1: If 3² is a factor of k, then a ≥ 2
So, a = 2 ---> b = 1
--> k = (3²)*7

Sufficient

Statement 1: If 7² is not a factor of k, then b < 2
So, b = 1 ---> a = 2
--> k = (3²)*7

Sufficient

The correct answer is D.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
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by gaurav_gaur » Sat Apr 27, 2013 11:18 pm
Thanks Anju.
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by seamaster1 » Sun Apr 28, 2013 1:08 am
Dear Gaurav_gaur, Dear Anju
Thank you for your attention and explanation.
It seems I've got the wrong question so I can not understand the problem.
Now it is clear.
Once again thanks a lot.
Cheers.
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by seamaster1 » Sun Apr 28, 2013 1:08 am
Dear Gaurav_gaur, Dear Anju
Thank you for your attention and explanation.
It seems I've got the wrong question so I can not understand the problem.
Now it is clear.
Once again thanks a lot.
Cheers.
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Junior | Next Rank: 30 Posts
Posts: 18
Joined: Wed Dec 19, 2012 8:17 pm

by seamaster1 » Sun Apr 28, 2013 1:09 am
Dear Gaurav_gaur, Dear Anju
Thank you for your attention and explanation.
It seems I've got the wrong question so I can not understand the problem.
Now it is clear.
Once again thanks a lot.
Cheers.
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