There are typos in your post. The statements should read as follows:

(1) 3^2 is a factor of k
(2) 7^2 is not a factor of k

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If a number n has 2 prime factors, the number can be prime factorized as (a^x)(b^y), where a and b are the prime factors, and x and y are integers.

The total number of factors n must have is (x+1)(y+1).

For eg., if n = 24 = (3^1)(2^3), then number of factors for n = (1+1)(3+1) = 8.

EDIT: Ian posted the theory and explanation to this here:

https://www.beatthegmat.com/what-s-your- ... 64-15.html


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In this question, k = (3^x)(7^y) and we need to the value of k.

since we know k has 6 factors, then (x+1)(y+1) = 6. so we can have two possibilites.

(i) x = 2, y=1, OR
(ii) x=1, y=2


Statement 1: 3^2 is a factor of k

from here we know x is definitely 2, and y must equal to 1. Sufficient.

Statement 2: 7^2 is not a factor of k

from here, we know that y cannot be 2, so y must equal to 1. If y = 1, then x = 2 (case (i)). Sufficient.

Choose D.

-BM-

OOps u r right BM.

And thanks for the explanation.

rgds