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    Question

    The product of two positive integers is 2646. If their

    HCF is 7 and their sum is 105, then find the difference between the numbers.
    A 11 Correct Answer Incorrect Answer
    B 16 Correct Answer Incorrect Answer
    C 21 Correct Answer Incorrect Answer
    D 26 Correct Answer Incorrect Answer

    Solution

    Let the numbers be 7a and 7b

    Then:
    7a × 7b = 2646 ⇒ ab = 54 ...............(1)
    7a + 7b = 105 ⇒ a + b = 15

    Put a = (15 - b) in (1):
    (15 - b) × b = 54
    ⇒ 15b - b² = 54
    ⇒ b² - 15b + 54 = 0
    ⇒ b² - 6b - 9b + 54 = 0
    ⇒ b(b - 6) - 9(b - 6) = 0
    ⇒ (b - 6)(b - 9) = 0

    So, b = 6 or 9
    Then, numbers are 42 and 63
    Required difference = 21

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