Question

Replace * by a digit so that 653*47 is divisible by 11

Answer 1

Each number is assigned odd and even position starting from ones place.
i.e.

6 5 3 * 4 7
e o e o e o

Sum of odds (o) =5+*+7=12+*
Sum of evens(e)=6+3+4=13

Difference between odd and even should be 0 or multiple of 11.
Taking difference we get
(13+*)-(12)
=1+*

So * is 1.

Therefore the digit divisible by 11 is 653147.

Proof
Sum of o = 5+1+7=13
Sum of e = 6+3+4=13
So difference is 0.
Thus divisible by 11.

653147÷11=59377.