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Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11: 92 __ 389

Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11: 
92 __ 389 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5870 Points
2 months ago
Dear Student

Let ‘a’ be placed here
Sum of its digits at odd places = 9 + 3 + 2
= 14Sum of its digits at even places = 8 + a + 9
= 17 + a
Difference = 17 + a–14
=3 +a
The difference should be 0 or a multiple of 11, then the number is divisible by 11
If 3 + a = 0
a = -3
But it cannot be a negative
Taking a closest multiple of 11 which is near to 3
It is 11 which is near to 3
Now, 3 + a = 11
a = 11–3
a=8
Therefore the required digit is 8

Thanks

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