A number is divisible by 11 if the difference between the sums of the digits in odd and even places respectively is

### Concept & Logic The divisibility rule for 11 relies on the alternating sum of its digits. For any integer to be divisible by 11, the difference between the sum of the digits in its odd positions and the sum of the digits in its even positions must be exactly 0 or a multiple of 11 (such as 11, 22, 33). ### Step-by-Step Solution This is a direct theoretical question testing knowledge of foundational divisibility rules. * The question states: "A number is divisible by 11 if the difference between the sums of the digits in odd and even places respectively is..." * According to the standard mathematical rule for divisibility by 11, this difference must equate to 0, 11, 22, etc. * Looking at the options, only option (d) correctly identifies this requirement. ### Exam Strategy & Shortcut There is no calculation required here. Memorizing the fundamental divisibility rules for numbers 2 through 11 is mandatory for competitive exams, as it allows you to answer definitive theoretical questions in under five seconds. ### Common Pitfall A common mistake is confusing this rule with the rule for 3 or 9, where the sum of *all* digits is considered. Test-takers might wrongly guess options related to 3 if they misremember the rule structure. ### Final Answer Therefore, the correct answer is **zero or a multiple of 11**.