# value of A and B

• Dec 22nd 2012, 05:00 AM
rcs
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?
• Dec 22nd 2012, 05:10 AM
Plato
Re: value of A and B
Quote:

Originally Posted by rcs
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 $\displaystyle B=0\text{ or }B=5~?$
• Dec 22nd 2012, 05:12 AM
jakncoke
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 $\displaystyle \{0,1,2,3,4,5,6,7,8,9\}$

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
• Dec 22nd 2012, 07:29 AM
rcs
Re: value of A and B
Quote:

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

Do you know that $\displaystyle B=0\text{ or }B=5~?$

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
• Dec 22nd 2012, 07:33 AM
rcs
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
• Dec 22nd 2012, 07:58 AM
Plato
Re: value of A and B
Quote:

Originally Posted by rcs
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

• Dec 22nd 2012, 08:03 AM
ILikeSerena
Re: value of A and B
Quote:

Originally Posted by rcs
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?
• Dec 22nd 2012, 06:20 PM
rcs
Re: value of A and B
Quote:

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

yeah