The smallest one digit number, which must be added to 803642 in order to obtain a multiple of 9, is:

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answer is D.

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Detailed Solution

Concept- We will find the remainder of 803642 when it will be divided by 9. Then, find by how many numbers does the given number lack to become the multiple of 9, so basically the difference between the given number and the nearest multiple of 9 to the given number in the question.
The number is 803642.
The sum of its digit

= 8 + 0 + 3 + 6 + 4 + 2 = 23

As, 23 is not divisible by 9.
Therefore, we will get some non-zero remainder, r where

1 \leq r \leq 8

After dividing 803642 by 9, we get

\Rightarrow \frac{803642}{9} = 89293

≃ 89294

So, the number after 803642 is a multiple of 9

= 803637 + 9 = 803646

Now, the difference is 4 between 803642 and 803646.
Therefore, 4 is the number which should be added with 803646 to get the multiple of 9.
Because, it is clear that