Q16. 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)?
Detailed Solution
Given the ranges for x and y: 4 ≤ x ≤ 8 2 ≤ y ≤ 7 To find the maximum value of (x + y): We take the maximum possible value for x and the maximum possible value for y. Max(x + y) = Max(x) + Max(y) = 8 + 7 = 15.
To find the minimum value of (x - y): We take the minimum possible value for x and subtract the maximum possible value for y. Min(x - y) = Min(x) - Max(y) = 4 - 7 = -3. Now, we need to find the ratio of the maximum value of (x + y) to the minimum value of (x - y): Ratio = Max(x + y) / Min(x - y) = 15 / (-3) = -5.
Since -5 is not listed in options (a), (b), or (c), the correct answer is (d) None of the above. This question tests basic understanding of inequalities and how to find maximum/minimum values of expressions involving ranges, a common concept in UPSC CSAT.
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