Question

Find digits A and B in the number below so the folling condition are true. The 5-digit number must be divisible by 4. The 5-digit number must be divisible by 9. Digit A cannot be the same as Digit B.


12A3B

Explain the steps you followed to solve the problem.

Answer 1

If a number is divisible by 9, the sum of its digits is too. That is, they must add up to a multiple of 9.

6+A+B = 9k
so,
A+B = 9k-6
The most they can be is 18, so they must add up to 12 or 3.

3B must be a multiple of 4, since xxx00 is. So, 3B must be 32 or 36. Can't be 36, because that would make B=6 so A=6.

So, B = 2 and A=1

12132 = 4*3283 = 9*1348