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Math Help - value of A and B

  1. #1
    rcs
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    value of A and B

    If A and B are digits and the number 2A35B is divisible by 15. What is the value of A and B and the largest value of A and B?


    can anybody help me on this problem?
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    Re: value of A and B

    Quote Originally Posted by rcs View Post
    If A and B are digits and the number 2A35B is divisible by 15. What is the value of A and B and the largest value of A and B?
    What do you know about the sum of the digits?

    Do you know that B=0\text{ or }B=5~?
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    Senior Member jakncoke's Avatar
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    Re: value of A and B

    Since 2A35B is divisible by 15, it is divisible by 3 and 5.
    Since it is divisible by 5, the last number must be 0 or 5.

    Assume the last number is 0, then since it is divisible by 3, the sum of the numbers should be divisible by 3
    2+A+3+5+0 = (10 + A) is divisible by 3, and A can only be from  \{0,1,2,3,4,5,6,7,8,9\}

    Do the same for if last number is 5.

    All the possible numbers
    20355
    23355
    26355
    29355

    22350
    25350
    28350

    Largest A = 9, Largest B = 5
    Largest num = 29355
    Last edited by jakncoke; December 22nd 2012 at 05:15 AM.
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    rcs
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    Re: value of A and B

    Quote Originally Posted by Plato View Post
    What do you know about the sum of the digits?

    Do you know that B=0\text{ or }B=5~?
    it is a typo.

    this is correct statement of problem:

    If A and B are digits and the number 2A35B is divisible by 15. What is the value of A and B and the largest value of A + B?

    i have difficulty when letters are included in a digit of the number...

    i cannot imagine how it is being applied sir... need your help on this
    thanks
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  5. #5
    rcs
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    Re: value of A and B

    from the book i read the answer is 14... but sad to say that i dont know how they do that... that is why i ask help from here.. thanks
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    Re: value of A and B

    Quote Originally Posted by rcs View Post
    it is a typo.

    this is correct statement of problem:

    If A and B are digits and the number 2A35B is divisible by 15. What is the value of A and B and the largest value of A + B?

    i have difficulty when letters are included in a digit of the number...

    i cannot imagine how it is being applied sir... need your help on this
    thanks

    Read reply #3 carefully. It is complete and correct.
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  7. #7
    Super Member ILikeSerena's Avatar
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    Re: value of A and B

    Quote Originally Posted by rcs View Post
    from the book i read the answer is 14... but sad to say that i dont know how they do that... that is why i ask help from here.. thanks
    Hmm, 14.... did they ask perhaps for the largest sum of A and B?
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  8. #8
    rcs
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    Re: value of A and B

    Quote Originally Posted by ILikeSerena View Post
    Hmm, 14.... did they ask perhaps for the largest sum of A and B?
    yeah
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