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UPSC Prelims 2025 CSAT, question 26

Topic: Arithmetic

Q26

If 4≤x≤84 \le x \le 8 and 2≤y≤72 \le y \le 7, then what is the ratio of maximum value of (x+y)(x+y) to minimum value of (x−y)(x-y) ?

  1. (a) 66
  2. (b) 152\frac{15}{2}
  3. (c) −152-\frac{15}{2}
  4. (d) None of the aboveCorrect answer

Solution.

Answer: (d) None of the above

  1. Given 4≤x≤84 \le x \le 8 and 2≤y≤72 \le y \le 7, the maximum value of (x+y)(x + y) is 8+7=158 + 7 = 15.
  2. The minimum value of (x−y)(x - y) occurs when xx is smallest and yy is largest, giving 4−7=−34 - 7 = -3.
  3. The ratio of the maximum value of (x+y)(x + y) to the minimum value of (x−y)(x - y) is 15−3=−5\frac{15}{-3} = -5, which is not among (a), (b), or (c), so (d) None of the above is correct.