Step 1: Evaluate Option A
If x=25 and y=40, then x is not greater than y.
Therefore, Option A is not always correct.
Step 2: Evaluate Option B
If x=25 and y=40, then y−x=40−25=15, which is not greater than 15.
Therefore, Option B is not always correct.
Step 3: Evaluate Option C
If x=25 and y=40, then y−x=40−25=15, which is less than or equal to 15.
If x=26 and y=39, then y−x=39−26=13, which is also less than or equal to 15.
Therefore, Option C is always correct.
Step 4: Evaluate Option D
If x=25 and y=40, then x+y=25+40=65, which satisfies the condition.
However, if x=28 and y=30, then x+y=28+30=58, which is less than 65.
Therefore, Option D is not always correct.
Conclusion: The statement that is always correct is Option C: