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  1. (22)4 + (101)3 - (20)5 = (x)4 + (4)x+1 where x > 4. The value of x is

    2. A.
    6
    B.
    4
    C.
    12
    D.
    8

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    Answer : Option C

    Explanation :

    (22)4 + (10)10 - (10)10 = (22)4

    Since x > 4, i.e. all the number systems with base greater than 4.

    All these will contain symbol '4' which will have same value in all bases.

    Converting 4 into base '4'

    system (4)10 (10)4

    Now (22)4 = (x)4 + (10)4

    ∴ (x)4 = (22)4 - (10)4 = (12)4

    ∴ x = 12.

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