Thread: value of A and B

1. 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?

2. Re: value of A and B

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 $B=0\text{ or }B=5~?$

3. 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

4. Re: value of A and B

Originally Posted by Plato
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

5. 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

6. Re: value of A and B

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