Divisibility by 11 — Among the following eight-digit numbers, identify which one is divisible by 11 using the alternating-sum rule.

Introduction / Context:
The divisibility rule for 11 avoids long division by converting the digits into an alternating sum. If the alternating sum is a multiple of 11 (including 0), the number is divisible by 11. We apply this rule to each option to find the only correct choice.

Given Data / Assumptions:

• Candidates: 45678940, 54857266, 87524398, 93455120.
• Rule: sum of digits in odd positions minus sum in even positions must be 0 or a multiple of 11.
• Counting positions from left as position 1.

Concept / Approach:
Compute alternating sum quickly, preferably grouping digits to reduce errors. Because we only need one correct option, stop once you find a number with alternating sum 0 or ±11, ±22, etc., but verify carefully to avoid slips.

Step-by-Step Solution:
Example for 93455120: positions (from left) 1..8 → (9−3+4−5+5−1+2−0) = 11 − 6 − 1 + 2 = 6? Recheck cleanly: (9 − 3) + (4 − 5) + (5 − 1) + (2 − 0) = 6 − 1 + 4 + 2 = 11.Alternating sum = 11, which is a multiple of 11 → divisible by 11.The other options produce alternating sums not equal to a multiple of 11 on careful calculation.

Verification / Alternative check:
A second pass or quick calculator confirms only 93455120 satisfies the 11-rule. If in doubt, compute modulo 11 directly for each candidate.

Why Other Options Are Wrong:
45678940, 54857266, and 87524398 each yield an alternating sum that is not a multiple of 11, so they fail the rule.

Common Pitfalls:
Mislabeling odd/even positions; dropping a digit in the alternating sum; stopping early without confirming the multiple-of-11 condition.

Final Answer:
93455120