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      Question

      The sum of two numbers is 444 and their HCF is 37. Find

      all the possible pairs of such numbers?
      A (1, 11), (5, 7) Correct Answer Incorrect Answer
      B (6, 6), (4, 8) Correct Answer Incorrect Answer
      C (3,9) , (8,4) Correct Answer Incorrect Answer
      D (5, 7), (9, 3) Correct Answer Incorrect Answer

      Solution

      HCF of two numbers = 37 Hence, numbers are multiples of 37. Let the numbers be 37a and 37b, where ‘a’ and ‘b’ are prime numbers to each other. According to the question ∴ 37a + 37b = 444 (a + b) = 12 ∴ Required possible pairs of values of ‘a’ and ‘b’ are prime to each other are (1, 11) and (5, 7).

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