X = 2^a * 3^b, while Y = 3^c * 5^d, where a, b, c, d are all positive

From stem: Definition of GCD: GCD is the product of common primes in their least power.
The only prime factor common to X and Y is 3. So, the GCD of X and Y will be 3^b is b < c and the GCD will be 3^c if c < b.

Statement 1: LCM of X and Y = (2^3 * 3^2 * 5^4)
Definition of LCM: LCM is the product of all primes in their highest power.
Relevant information: The highest power of 3 between X and Y is 3^2 as the LCM contains 3^2.
Possibility 1: The two powers of 3 found in X and Y could both be 3^2. In that case, the GCD will be 3^2.
Possibility 2: The two powers of 3 found in X and Y could be 3^1 and 3^2. In that case, the GCD will be 3^1.

With the information in statement 1, we will not be able determine whether it is 3^2 or 3^1.
Statement 1 ALONE is NOT sufficient.

Statement 2:a, b, c, d are all distinct from each other.
It leaves the door open to infinite possibilities.
Statement 2 ALONE is NOT sufficient.

Combining the 2 statements: From statement 2, if a, b, c, and d are distinct, b and c will have to be different numbers.
From statement 1, we narrowed down values of b and c to be both 2 or one 1 and the other 2.
If b and c are distinct, both cannot be same. So, that rules of possibility 1 of statement 1.
We are left with only possibility 2 that satisfies both conditions. So, the GCD is 3^1.

TOGETHER staements SUFFICIENT.
Choice C.