Sakib Knows The Number!

Ragib: I got digits of a 2 digit number
Sakib: Is it an odd?
Ragib: Yes. Moreover, the sum of the digits of the number is a prime!
Sakib: The difference of the digits of the number is also a prime?
Ragib: Of course! Last of all, the multiply of the digits is equal to one of the digits!!
Sakib: Oh no! I know the number. It’s your roll number!
What is that number!

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masterminded Expert Asked on 6th June 2016 in Math Puzzles.
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  • 4 Answer(s)
    Best answer

    The digits may be 1,2,3,4,5,6,7,8,9,0.
    Since two digit number, 0 can only be put in the second digit position.
    But that will make the number even. So 0 is not any of the digits!!
    1* any digit=1 or the digit
    2*any digit(not 1) = not 2 or not the digit
    3*any digit(not 1) = not 3 or not the digit
    4*any digit(not 1) = not 4 or not the digit
    5*any digit(not 1) = not 5 or not the digit
    6*any digit(not 1) = not 6 or not the digit
    7*any digit(not 1) = not 7 or not the digit
    8*any digit(not 1) = not 8 or not the digit
    9*any digit(not 1) = not 9 or not the digit
    So its clear one digit is 1.
    So the number may be 11,21,31,41,51,61,71,81,91.
    But the sum of the 2 digit is also a prime!
    So 31,51,71,81,91 will be ignored!
    Now the answer may be 11,21,41,61
    But the difference of the digit also is a prime!!
    So 11,21 will be ignored!!!!
    So the answer is 41/61…..
    What a puzzle…!!!

    LOL Guru Answered on 7th June 2016.
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    61

    Yodha Expert Answered on 6th June 2016.
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    41

    venkatarameshbabu Starter Answered on 7th June 2016.
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    numbers that follow  odd and sum of digits is a prime are :11,21,23,25,29,41,43,49,61,65,67,83,85.
    among these numbers follows “difference of digits also prime” are : 25,29,41,47,49,61,83,85.
    last but not least , product of digits is same as one of it’s  digits means one digit should be 1.
    So Answer is 41 or 61.

    Sathya Curious Answered on 26th July 2016.
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