Here is my solution:

Question: Does K have at-least 3 different positive prime factors.

Statement 1: \(\frac{k}{15}\) is an integer.

Hence the values of k are multiples of 15 such as 15,30,45...

Factors of 15 = 5 and 3 (2 factors)

Factors of 30 = 5 , 3 and 2 (3 factors)

Hence not sufficient.

Statement 2: \(\frac{k}{10}\) is an integer

Hence the values of k are multiples of 10 such as 10,20,30

Factors of 10 = 5 and 2 (2 factors)

Factors of 30 = 5 , 3 and 2 (3 factors)

Hence not sufficient.

Stmt 1 + Stmt 2:

k should be multiples of 10 and 15 such as 30,60...

All these values have atleast 3 positive different prime factors.

Hence C.

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