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 ?

(a) x is greater than y
(b) (y – x) is greater than 15
(c) (y – x) is less than or equal to 15 ✓ UPSC's answer
(d) (x + y) is greater than or equal to 65

Why the answer is (c)

• Given the constraints, the minimum value of x is 25 and the maximum value of y is 40.

• To determine the maximum possible value of (y - x), we use the maximum y and minimum x: 40 - 25 = 15.

• Since y cannot exceed 40 and x cannot be less than 25, the difference (y - x) can never be greater than 15.

• Therefore, (y - x) is always less than or equal to 15.

• This confirms that option (c) is the only statement that holds true for all valid values of x and y.

Why the other options are wrong

(a) x is greater than y: x is not always greater than y, as x can be 25 and y can be 40, making y greater than x.
(b) (y – x) is greater than 15: (y - x) is not always greater than 15; in fact, it is never greater than 15, and can be negative if x > y.
(d) (x + y) is greater than or equal to 65: (x + y) is not always greater than or equal to 65, as the minimum sum is 25 + 0 (if y can be 0) or 25 + 1 (if y is positive integer), which is less than 65.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.