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?

Correct Option (C)

Given the conditions:

• x ≥ 25
• y ≤ 40

To determine the maximum possible value of the expression (y - x), we must maximize the value of y and minimize the value of x, subject to the given constraints.

• The maximum value y can take is 40.
• The minimum value x can take is 25.

Therefore, the maximum value of (y - x) is 40 - 25 = 15.

For any other valid combination of x and y within the specified ranges, (y - x) will be less than or equal to 15. For example, if x = 26 and y = 40, then (y - x) = 14. If x = 25 and y = 39, then (y - x) = 14.

Thus, the statement (y - x) is less than or equal to 15 is always correct.

Incorrect Options:

Option A: x is greater than y

This statement is not always correct. Consider the case where x = 25 and y = 40. Here, x is not greater than y (25 is not > 40). While x could be greater than y for some values (e.g., x = 30, y = 28), it is not universally true under the given conditions.

Option B: (y - x) is greater than 15

As derived for the correct option, the maximum possible value for (y - x) is 15. Therefore, (y - x) can never exceed 15. This statement is always incorrect.

Option D: (x + y) is greater than or equal to 65

This statement is not always correct. To test this, consider a scenario where y is significantly less than 40, while still satisfying y ≤ 40. For example, if x = 25 (minimum value for x) and y = 20 (which is ≤ 40), then (x + y) = 25 + 20 = 45. Since 45 is not greater than or equal to 65, this option is not always true.