What are the smallest digit and the greatest digit that can be inserted as the first digit in the number 6724, so that the number formed is divisible by 3?

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3, 9

2, 8

1, 9

2, 3

answer is B.

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Detailed Solution

It is given that by inserting a smallest digit and the greatest digit as the first digit in the number 6724, the number formed will be divisible by 3.
When the sum of the digits in a number are divisible by 3, then the number is also divisible by 3.
Sum of the given digits is,
6 + 7 + 2 + 4 = 19.
If we add 2 then the digit is divisible by 3.
i.e., 19 +2 = 21.
Hence, 2 is the smallest digit.
If we add 8 then the digit is divisible by 3.
i.e., 19 +8 = 27.
Hence, 8 is the largest digit.
The smallest digit is 2 and can be written as 26724 and the greatest digit is 8 and can be written as 86724, where 26724 and 86724 are divisible by 3.
Therefore, option 2 is correct.

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