Final answer:
Option (C), If z is divisible by both x and y, it must also be divisible by xy. Options A, B, and D are not necessarily divisors of z.
Step-by-step explanation:
If z is divisible by both x and y, it must also be divisible by xy. The product of x and y is their greatest common divisor, which means that z is divisible by both x and y, so it must also be divisible by their common divisor, xy.
Option A, x - y, is not necessarily a divisor of z. For example, if x = 6 and y = 3, z = 6 and x - y = 3, which does not divide 6.
Option B, x + y, is also not necessarily a divisor of z. For example, if x = 6 and y = 4, z = 12 and x + y = 10, which does not divide 12.
Option D, x/y, is not necessarily a divisor of z either. For example, if x = 6 and y = 2, z = 6 and x/y = 3, which does not divide 6.