What will be the smallest natural number to be filled in the blank for the number ’23_45678’ to be divisible by 22?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 7
Let the number in the blank be x
For this number to be divisible by 22, it has to be divisible by 2 and 11.
To be divisible by 11, (8 + 6 + 4 + 3) - (7 + 5 + x + 2) has to be a multiple of 11 or 0
⇒ (8 + 6 + 4 + 3) - (7 + 5 + x + 2) = 21 - 14 - x ⇒ 7 - x
'7 - x' cannot be a multiple of 11. Thus it has to be zero.
7 - x = 0 ⇒ x = 7