If the 6-digit number 7B256A is divisible by 11, then which of the following…

Concept: A number is divisible by 11 exactly when the difference between the sum of its digits in the odd positions and the sum of its digits in the even positions (counted from either end) is 0 or a multiple of 11.

1. Label the digits of 7B256A by position from the left: position 1 = 7, position 2 = B, position 3 = 2, position 4 = 5, position 5 = 6, position 6 = A.

2. Sum the digits in the odd positions (1, 3, 5): 7 + 2 + 6 = 15.

3. Sum the digits in the even positions (2, 4, 6): B + 5 + A.

4. Form the alternating difference: 15 − (B + 5 + A) = 10 − A − B.

5. For divisibility by 11 this difference must be 0 or a multiple of 11. Since A and B are single digits (0–9), A + B can only range from 0 to 18, so 10 − A − B = 0 is the only possibility in range — hence A + B = 10.

Cross-check: With A = 4, B = 6, the number is 762564, and 762564 ÷ 11 = 69324 exactly (odd-position sum 7 + 2 + 6 = 15 equals even-position sum 6 + 5 + 4 = 15, difference 0). With A = 9, B = 1, the number 712569 = 11 × 64779, again with A + B = 10.

So the equation that correctly relates A and B whenever 7B256A is divisible by 11 is A + B = 10.