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)?

1. A. 6
2. B. 15/2
3. C. –15/2
4. D. None of the above

Answer: D

Explanation

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.