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For a number to be divisible by 11, which of the following must be true?

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Question: For a number to be divisible by 11, which of the following must be true?

Options:

  1. The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
  2. The number must be even
  3. The number must end in 1
  4. The sum of the digits must be divisible by 11

Correct Answer: The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11

Solution: 

A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or divisible by 11.

For a number to be divisible by 11, which of the following must be true?

Practice Questions

Q1
For a number to be divisible by 11, which of the following must be true?
  1. The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
  2. The number must be even
  3. The number must end in 1
  4. The sum of the digits must be divisible by 11

Questions & Step-by-Step Solutions

For a number to be divisible by 11, which of the following must be true?
  • Step 1: Identify the digits of the number you want to check for divisibility by 11.
  • Step 2: Label the positions of the digits starting from the right. The rightmost digit is position 1 (odd), the next is position 2 (even), and so on.
  • Step 3: Add up all the digits that are in odd positions. This is your 'sum of odd positions'.
  • Step 4: Add up all the digits that are in even positions. This is your 'sum of even positions'.
  • Step 5: Calculate the difference between the 'sum of odd positions' and the 'sum of even positions'.
  • Step 6: Check if this difference is 0 or if it can be divided evenly by 11 (meaning there is no remainder).
  • Step 7: If the difference is 0 or divisible by 11, then the original number is divisible by 11.
  • Divisibility Rule for 11 – A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or divisible by 11.
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