If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x - y) ?

(a) 6
(b) 15/2
(c) - 15/2
(d) None of the above ✓ UPSC's answer

Why the answer is (d)

• To find the maximum value of (x + y), we must maximize both variables within their given ranges: x_max = 8 and y_max = 7.

• The maximum value of (x + y) is therefore 8 + 7 = 15.

• To find the minimum value of (x - y), we must minimize x and maximize y: x_min = 4 and y_max = 7.

• The minimum value of (x - y) is therefore 4 - 7 = -3.

• The ratio of the maximum value of (x + y) to the minimum value of (x - y) is 15 / (-3) = -5.

• Since -5 is not listed among options (a), (b), or (c), the correct choice is (d) None of the above.

Why the other options are wrong

(a) 6: Option (a) 6 is incorrect because the calculated ratio is -5, not 6.
(b) 15/2: Option (b) 15/2 is incorrect because it likely confuses the maximum sum (15) with a different denominator or ignores the negative sign of the minimum difference.
(c) - 15/2: Option (c) -15/2 is incorrect because the denominator is -3, not -2, resulting in a ratio of -5.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.