Question

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

Answer 1

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.

Complete step-by-step answer:
The given number is 803642. Let us first divide it by 9. It is very clear that 803642 is not exactly divisible by 9 as the sum of its digits is 8+0+3+6+4+2 = 23 which is not divisible by 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 \[89293\cdot 9=803637\].
Therefore, the next multiple of 9 will be just 9 added with the previous multiple.
So, the number just after 803642 which is a multiple of 9 is \[803637+9=803646\].
Now the difference is \[803646-803642=4\]
So, 4 is the number which needs to be added with 803646 in order to get a multiple of 9.
Because, it is clear that \[803642+4=803646=9\cdot 89294\]
So, here the correct option to this question is option (d) 4

Note: A number is divisible by 9 if and only if the sum of the digits of the number is divisible by 9. Here in this problem, we can easily get the answer by adding the options with 803642 and checking the sum of the digits whether it is divisible by 9 or not.