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    Question

    The sum of two numbers is 99 and their HCF is 9. Total

    number of such pairs of numbers is?     
    A 4 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 5 Correct Answer Incorrect Answer
    D 7 Correct Answer Incorrect Answer

    Solution

    According to question, HCF =9 Then, the two number will be 9a,9b Also, 9a+9b = 99, or , a+b =11 All possible pairs of positive integers  a and b are (1,10),(2,9),(3,8),(4,7), and (5,6). Hence, required pairs of positive integers are = (9,90),(18,81),(27,72),(36,63), and (45,54). Hence, the number of pairs of positive integers is 5.

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