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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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