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    Question

    What is least number which when successively divided by

    6, 4 and 4 leaves a remainder 5, 3 and 3 respectively?
    A 95 Correct Answer Incorrect Answer
    B 177 Correct Answer Incorrect Answer
    C 57 Correct Answer Incorrect Answer
    D 17 Correct Answer Incorrect Answer

    Solution

    ATQ,

    First condition: N≡5(mod6). Let N=6a+5. Second condition: Quotient a≡3(mod4). Let a=4b+3. Substituting: N=6(4b+3)+5=24b+18+5=24b+23. Third condition: Quotient b≡3(mod4). Let b=4c+3. Substituting: N=24(4c+3)+23=96c+72+23=96c+95. Smallest N: Set c=0: N=96(0)+95=95. The least N is 95.

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