What should be the missing digit so that the number 275_476 becomes exactly divisible by 11?

For a number to be divisible by 11, difference between the sum of digits at odd places and even places (starting from right to left) should be divisible by 11.

Let the number be = $$275x476$$

Sum of digits at odd places = $$6 + 4 + 5 + 2 = 17$$

Sum of digits at even places = $$7 + x + 7 = (14 + x)$$

Difference = $$17 - 14 - x = 3 - x$$

Now, for $$(3 - x)$$ to be divisible by 11, it should be equal to 11 or 0 but if it is equal to 11, then $$x$$ will be negative, thus

=> $$3 - x = 0$$

=> $$x = 3 - 0 = 3$$

=> Ans - (D)