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]
Positive Interger
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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
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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Your analysis is flawless as per the problem posted.gaurav_gaur wrote:Can anyone please let me know if I am missing anything here.
However, I think the actual problem is as follows...
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.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
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
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Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
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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.
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
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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.
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.
-
- Junior | Next Rank: 30 Posts
- Posts: 18
- Joined: Wed Dec 19, 2012 8:17 pm
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.
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.