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      Question

      The product of two positive integers is 3630. If their

      HCF is 11 and their sum is 143, then find the difference between the numbers.
      A 71 Correct Answer Incorrect Answer
      B 73 Correct Answer Incorrect Answer
      C 75 Correct Answer Incorrect Answer
      D 77 Correct Answer Incorrect Answer

      Solution

      Let the numbers be 11a and 11b

      Then:
      11a × 11b = 3630 ⇒ ab = 30 ...............(1)
      11a + 11b = 143 ⇒ a + b = 13

      Put a = (13 - b) in (1):
      (13 - b) × b = 30
      ⇒ 13b - b² = 30
      ⇒ b² - 13b + 30 = 0
      ⇒ b² - 3b - 10b + 30 = 0
      ⇒ b(b - 3) - 10(b - 3) = 0
      ⇒ (b - 3)(b - 10) = 0

      So, b = 3 or 10
      Then, numbers are 33 and 110
      Required difference = 77

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