If the six digit number 15x1y2 is divisible by 44, then (x + y) is equal to:

To solve this problem, we need to know that a number is divisible by 44 if and only if it is divisible by both 4 and 11 (since 44 is the product of 4 and 11).

1. Check for divisibility by 4: A number is divisible by 4 if the number formed by the last two digits is divisible by 4. Here, the last two digits form the number 2y. For this number to be divisible by 4, y must be 2 or 6.

2. Check for divisibility by 11: A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or a number divisible by 11. Here, the sum of the digits at odd places is 1 + x + 1 + 2 = 4 + x, and the sum of the digits at even places is 5 + 1 + y = 6 + y. The difference between these two sums is (4 + x) - (6 + y) = x - y - 2. For this number to be divisible by 11, x - y must be 2 or -9.

3. Combine the results from steps 1 and 2: From step 1, we know that y is 2 or 6. From step 2, we know that x - y is 2 or -9. If y is 2, then x must be 4 (since 4 - 2 = 2). If y is 6, then x cannot be -3 (since -3 - 6 = -9 is not a valid digit). Therefore, the only solution is x = 4 and y = 2.

4. Find x + y: Since x = 4 and y = 2, x + y = 4 + 2 = 6. Therefore, x + y is equal to 6.