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    Question

    The product of two positive integers is 3630. If their

    HCF is 11 and their sum is 143, then find the difference between the numbers.
    A 71 Correct Answer Incorrect Answer
    B 73 Correct Answer Incorrect Answer
    C 75 Correct Answer Incorrect Answer
    D 77 Correct Answer Incorrect Answer

    Solution

    Let the numbers be 11a and 11b

    Then:
    11a × 11b = 3630 ⇒ ab = 30 ...............(1)
    11a + 11b = 143 ⇒ a + b = 13

    Put a = (13 - b) in (1):
    (13 - b) × b = 30
    ⇒ 13b - b² = 30
    ⇒ b² - 13b + 30 = 0
    ⇒ b² - 3b - 10b + 30 = 0
    ⇒ b(b - 3) - 10(b - 3) = 0
    ⇒ (b - 3)(b - 10) = 0

    So, b = 3 or 10
    Then, numbers are 33 and 110
    Required difference = 77

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