Subject

    Quantitative Aptitude

    Topic

    Number

    How many remainders are possible if 16n16^n is divided by 9 for any positive integral value of n ?

    ক)
    1
    খ)
    5
    গ)
    3
    ঘ)
    4

    Explanation

    When 16n16^n is divided by 9, we have 1619\frac{16^1}9 , remainder = 7 1629\frac{16^2}9 remainder = 4 1639\frac{16^3}9 remainder = 1 1649\frac{16^4}9 , remainder = 7 1659\frac{16^5}9 remainder = 4 1669\frac{16^6}9 remainder = 1 So, we have cyclicity of 3 factors i.e 7,4,1. Hence only 3 remainders are possible.

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