C. Together, the answers are sufficient.
This can be solved using prime factorization. K is a multiple of 29. So, they share prime factors (29). Remember, K could have additional prime factors. But, it has at LEAST the same prime factors as 29.
We're trying to determine if KY is a multiple of 174. So, does KY share at least the same prime factors with 174 (2x3x29). We already know that K has 29 as a prime factor, so K and/or Y must have 2 and 3 as prime factors to be sufficient.
(1) Y shares factors with 27. So, they will share prime factors (3x3x3). This gives us one of the required values but not the other. Insufficient.
(2) K is divisivle by 2 without a remainder. So, K/2 = integer. K = 2 x integer. So, 2 is a prime factor of K. This gives us one of the required values but not the other.
(1) + (2) Sufficient. Together, we have the two required prime factors (2, 3).
