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.
