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    Question

    Find the greatest 3-digit number which when divided by 11

    or 16 leaves 3 as remainder.
    A 415 Correct Answer Incorrect Answer
    B 775 Correct Answer Incorrect Answer
    C 883 Correct Answer Incorrect Answer
    D 870 Correct Answer Incorrect Answer

    Solution

    ATQ,

    LCM of 11 and 16 = 176

    Let the required number be of the form:

    Number = 176 × k + 3

    We want the greatest 3-digit number:

    176k + 3 ≤ 999

    ⇒ 176k ≤ 996

    ⇒ k = 5 (since 176 × 5 = 880)

    ∴ Required number = 176 × 5 + 3 = 883

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