Q.)The remainder, when is divided by 19, is
[CAT 2004 Question, Remainder Question, Number System, CAT Question]
We know that
So, We can conclude from the above formulae that is always divisible by (a+b).
Hence , is always divisible by (15+19) = 38
Now, if any number is divisible by 38 , then that number will also be divisible by 19 as 38 is a multiple of 19.
Hence, the remainder obtained , when is divided by 19 = 0.
This can also be solved in another way :
This way also, we see that , it is divisible by 19. Hence, the remainder obtained is 0.