Akansha 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. 3^2 is a factor of k
b. 7^2 is not a factor of k
OA is D
Solution:
The integer k can be represented as (3^a)*(7^b) where a and b are certain positive integers.
Now, total number of factors of k is (a+1)*(b+1) = 6.
So the possible combinations of (a+1) and (b+1) are (1, 6),(2,3),(3,2), (6,1).
Or the possible combinations of a and b are (0,5), (1,2), (2, 1), (5,0).
Now, (0,5) and (5,0) are eliminated because both a and b have to be positive.
Let us now consider statement a. alone.
It means that a >= 2. Or the only feasible option is a = 2 and b = 1.
So, k = (3^2)*7 = 63.
Next consider statement b. alone.
It means that b < 2. Again the only feasible option is a = 2 and b = 1.
Or k = 63.
So, each statement alone is sufficient to answer the question.
The correct answer is (D).
