If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?

We have two constraints: x ≥ 25 (so the smallest x is 25) and y ≤ 40 (so the biggest y is 40). We need a statement that is 'Always True' [50].\n\nLet's check the difference (y - x) found in options B and C. To see how big this difference can get, we use the 'Extremal Principle' [53]. We take the biggest possible 'y' and subtract the smallest possible 'x'.\nMax(y - x) = Max(y) - Min(x) = 40 - 25 = 15.\n\nThis means the value of (y - x) can never go above 15. It will always be less than or equal to 15. This matches Option (C) perfectly.\n\nWe can do a quick sanity check on the others using the 'Counter-Example Method' [57]:\n(A) x > y: If we pick x=25 and y=40, x is clearly smaller. This fails.\n(B) (y - x) > 15: We just proved the maximum is 15. So it can't be greater. This fails.\n(D) (x + y) ≥ 65: Since y can be any number less than 40, let's pick y=0. Then x+y = 25+0 = 25. This is not ≥ 65. This fails.\n\nThe only mathematically certain answer is C.