QUESTION

# The smallest one digit number, which must be added to 803642 in order to obtain a multiple of 9 is a)1b)2c)3d)4

Hint: Find out first the remainder when 803642 is divided by 9. Now calculate 803642 is how much is deficient of being next multiple of 9.

Therefore, we will get some non-zero remainder, r where $1\le r\le 8$ after dividing 803642 by 9.
Now after division we get $803642=89293\cdot 9+5$
So the remainder is 5 here. We get that the number just below 803642 which is a multiple of 9 is $89293\cdot 9=803637$.
So, the number just after 803642 which is a multiple of 9 is $803637+9=803646$.
Now the difference is $803646-803642=4$
Because, it is clear that $803642+4=803646=9\cdot 89294$