I guess it is C.
1. 2*x*5*y is always even integer if x and y are integers. But for non integers, for example,x=1/3, y=1/3, the expression will not be an integer.
2. the first condition: 2 + x + 5 + y is an even integer if only x+y is an odd integer. Again, x=4/3 and y=2/3 make the result of the expression non integer value.
3. the second condition: x=4/3 and y=1/3 make the result of the expression non integer value.
4. two conditions. It is obviously that x+y and x-y can be integers only if non integers are x=a+0.5, y=b+0.5. (a and b are integers)
So, 1-st condition: x+y=a+b+1 is odd or a+b is even; 2-nd condition: a-b is odd. For any a,b It is impossible to satisfy both conditions if x or y are non integers. Therefore, C.
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