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SSC Quantitative Aptitude Number System and its Operations Question Bank Numbers and Their Principles (II)

  • question_answer
    When \[({{67}^{67}}+67)\] is divided by 68, the remainder is

    A) 1

    B) 63

    C) 66

    D) 67

    Correct Answer: C

    Solution :

    [c] We know that, when \[{{(a-1)}^{n}}\] is divided by a, then remainder \[={{(-1)}^{n}}\] Now, \[{{67}^{67}}+67={{(68-\text{1})}^{67}}+67\] \[\therefore \] When \[{{(68-\text{1})}^{67}}\] is divided by 68, then remainder \[={{(-\,1)}^{67}}=-1\] Thus, when \[{{67}^{67}}+67\] is divided by 68, then remainder                         \[=-\,1+67=66\]


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