If x is a multiple of 5, y is a factor of 16, and z is a factor of 40,

For this question we must consider a variety of cases...

If x is a multiple of 5, then some possible values of x include: 5, 10, 15, 20, 25,....
If y is a factor of 16, then some possible values of y are: 1, 2, 4, 8, 16
If z is a factor of 40, then some possible values of z are: 1, 2, 4, 5, 8, 10, 20, 40

Now that's check each statement...

I. xy is a multiple of z.
If x = 5, y = 1 and z = 10, then xy = 5
Since 5 is NOT a multiple of 10, statement I is not necessarily true.
This means we can eliminate B and E since they state that statement I is true.

II. xy is not a factor of z.
If x = 5, y = 1 and z = 10, then xy = 5
Since 5 IS a factor of 10, statement II is not necessarily true.
This means we can eliminate C since it states that statement II is true.

III. xy is a factor of z.
If x = 5, y = 1 and z = 1, then xy = 5
Since 5 is NOT a factor of 1, statement III is not necessarily true.
This means we can eliminate D since it states that statement III is true.

Answer: A