The smallest 1-digit number to be added to the 6-digit number 910300 so that it is completely divisible by 11 is:

Correct option is A

Given: 

The smallest 1-digit number to be added to the 6-digit number 910300 so that it is completely divisible by 11 is: 

Concept Used: 

To determine if a number is divisible by 11, we use the divisibility rule for 11, which states:

A number is divisible by 11 if the alternating sum of its digits is divisible by 11

Solution:   

Checking through option;

Option A: 5

New number = 910300 + 5 = 910305

Digits: 9, 1, 0, 3, 0, 5

Alternate sum = 9 - 1 + 0 - 3 + 0 - 5 = 0 divisible by 11

Option B: 2

910300 + 2 = 910302

Digits: 9 - 1 + 0 - 3 + 0 - 2 = 3 not divisible by 11

Option C: 9

910300 + 9 = 910309

Digits: 9 - 1 + 0 - 3 + 0 - 9 = -4  not divisible by 11

Option D: 6

910300 + 6 = 910306

Digits: 9 - 1 + 0 - 3 + 0 - 6 = -1  not divisible by 11 

Thus, smallest 1 - digit number is 5 which makes the number divisible by 11 

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