Write the smallest digit and the greatest digit in the blank space of the following number so that the number formed is divisible by 34765_2:

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1 and 9

3 and 8

3 and 9

0 and 9

answer is D.

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Detailed Solution

Concept- The divisibility rule of 3 states that if the sum of a number's digits is divisible by 3, then the number is divisible by 3. We can apply this concept to find the solution to the given problem.
Here, the number is 4765_2.
If the sum of the digits is divisible by three, the number is divisible by three.
When adding the digits, we get

If we add 0 to this, then the sum will become 24, which is divisible by 3 and we know 0 is the smallest number that can fill the missing space.
Similarly, if we add 9 to this, then the sum will become 33, which is divisible by 3 and we know 9 is the largest number that can make the given number divisible by 3.
Therefore, 0 and 9 are the smallest and largest numbers, respectively, which can be filled in the blank space so that the number formed is divisible by 3.
Hence, the correct answer is option 4) 0 and 9.

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