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

  • question_answer
    It is given that \[({{2}^{32}}+1)\] is exactly divisible by a certain number. Which of the following is also definitely divisible by the same number?

    A) \[({{2}^{16}}+1)\]

    B) \[({{2}^{16}}-1)\]

    C) \[7\times {{2}^{33}}\]

    D) \[{{2}^{96}}+1\]

    Correct Answer: D

    Solution :

    [d] Let \[{{2}^{32}}=x\] and let \[({{2}^{32}}+1)=(x+1)\] be divisible by a number N. Then, \[({{2}^{96}}+1)={{({{2}^{32}})}^{3}}+1=({{x}^{3}}+1)\] \[=(x+1)\,({{x}^{2}}-x+1),\] which is clearly divisible by N, since \[(x+1)\] is divisible by N.


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