8th Class Mathematics Playing with Numbers Question Bank Playing with Numbers

  • question_answer How many 5-digit numbers of the form AABAA is divisible by 33?

    A)  1                                

    B)  3                    

    C)  0                                

    D)  infinite

    Correct Answer: B

    Solution :

    We have AABAA is divisible by 33. So, it is divisible by both 3 and 11. \[\therefore \text{A + B + A - (A + A)=B}\] is divisible by 11. \[\Rightarrow B=0\] Also, A+A+B+A+A=4A+B is divisible by 3. \[\Rightarrow 4A\] is divisible by 3                   \[(\because B=0)\] \[\Rightarrow A\] is divisible by 3 Hence, possible values of A are 0, 3, 6, 9 But A can't be equal to zero. \[\therefore \] Number of possible 5-digit numbers are 3.

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