What is the number of ordered pairs (x, y) where x, y are positive integers such that the eight digit number 74x8935y is divisible by 11?

Correct option is D

Given:
The 8-digit number 74x8935y is divisible by 11.
x and y are positive integer digits from 1 to 9.
Formula Used:
Divisibility rule for 11: The difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.
Solution:
Let the positions be numbered from left to right: 1 to 8.
Sum of digits at odd positions (1st, 3rd, 5th, 7th) = 7 + x + 9 + 5 = 21 + x
Sum of digits at even positions (2nd, 4th, 6th, 8th) = 4 + 8 + 3 + y = 15 + y
Difference = (21 + x) - (15 + y) = 6 + x - y
For divisibility by 11, the difference must be 0 or 11.
Case 1: 6 + x - y = 0
y - x = 6
Since x and y are positive digits (1 to 9), the possible pairs (x, y) are:
(1, 7), (2, 8), (3, 9). This gives 3 pairs.
Case 2: 6 + x - y = 11
x - y = 5
The possible pairs (x, y) are:
(6, 1), (7, 2), (8, 3), (9, 4). This gives 4 pairs.
Total number of ordered pairs = 3 + 4 = 7.
Final Answer
So the correct answer is (d)