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Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-23

  • question_answer
    A six digit number is formed by repeating a three digit number, e.g. 256, 256 or 678, 678 etc. Any number of this form is always exactly divisible by

    A)  7                    

    B)  11   

    C)  13                   

    D)  1001

    Correct Answer: D

    Solution :

    The number (x y z x y z) can be written, after giving corresponding weightage of the places at the digits occur, as \[100000x+10000y+1000z+100\,x+10\,y+z\] \[=100100\,x+10010\,y+1001\,z\] \[=1001\,\,\left( 100x+10y+z \right)\] Since, 1001 is a factor, the number is divisible by 1001. \[7\times 11\times 3=1001\] As the number is divisible by 1001, it will also be divisible by all three namely 7, 11 and 13 and not only one of these because all three are factors of 1001. So, the answer is 1001.


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