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      Question

      HCF and LCM of two numbers are 13 and 455. If one number

      lies between 60 and 70, then the other number lies between
      A 50 and 60 Correct Answer Incorrect Answer
      B 70 and 80 Correct Answer Incorrect Answer
      C 80 and 90 Correct Answer Incorrect Answer
      D 90 and 10 Correct Answer Incorrect Answer

      Solution

      Let the numbers be 13m and 13n.
      13m x 13n = 13 x 455 = 13 x 13 x 35
      Or mn = 35
      The co-prime numbers whose product is 35 are (5,7) and (1,35)
      Hence, the no.s are 13 x 5 and 13 x 7 or 13 x 1 and 13 x 35
      Or 65 and 91 or 13 and 455
      Given that, one them lies between 60 and 70 ie 65,
      Then the other number is 91 which lies between 90 and 100

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