JMO --- numbers

Find the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and N are single digit integers?



Answer:

if a number is divisible by 8, then the first 3 numbers from right hand side should be divisible by 8.
i.e. 58N should be divisible by 8. This is possible only when N = 4

if a number is divisible by 11, then the difference between the sum of odd numbers and the sum of even numbers should be divisible by 11.
ie. odd places ---- 4 + 5 + 8 + 0 + 3 = 20
even places -----  8 + 4 + 4 + 9 + M = 25 + M 

difference = 25 + M - 20 = 5 + M 
Therefore, M must be 6.

so, M,N = 6,4 Answer