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Which of the following is a rule for divisibility by 11?

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Question: Which of the following is a rule for divisibility by 11?

Options:

  1. The last digit must be even
  2. 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
  3. The number must end in 1
  4. The number must be a two-digit number

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: 

For a number to be divisible by 11, 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.

Which of the following is a rule for divisibility by 11?

Practice Questions

Q1
Which of the following is a rule for divisibility by 11?
  1. The last digit must be even
  2. 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
  3. The number must end in 1
  4. The number must be a two-digit number

Questions & Step-by-Step Solutions

Which of the following is a rule for divisibility by 11?
  • Step 1: Identify the number you want to check for divisibility by 11.
  • Step 2: Write down the digits of the number in order from left to right.
  • Step 3: Label the positions of the digits starting from 1 (the leftmost digit is position 1, the next is position 2, and so on).
  • Step 4: Separate the digits into two groups: those in odd positions and those in even positions.
  • Step 5: Add up all the digits in the odd positions to get a sum.
  • Step 6: Add up all the digits in the even positions to get another sum.
  • Step 7: Find the difference between the sum of the odd-position digits and the sum of the even-position digits.
  • Step 8: Check if this difference is 0 or if it can be divided evenly by 11 (i.e., check if the difference is a multiple of 11).
  • Step 9: If the difference is 0 or a multiple of 11, then the original number is divisible by 11.
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