Divisibility Rule for 11

A number is divisible by 11 if the difference between the sum of its digits at odd places (from the right) and the sum of its digits at even places (from the right) is either 0 or a multiple of 11.

Testing the Options

Let's apply this rule to each given number:

Option 1: 332155

• Digits at odd places (1st, 3rd, 5th from right): 5, 1, 3. Sum = \( 5 + 1 + 3 = 9 \).
• Digits at even places (2nd, 4th, 6th from right): 5, 2, 3. Sum = \( 5 + 2 + 3 = 10 \).
• Difference: \( |10 - 9| = 1 \). Since 1 is not 0 or a multiple of 11, 332155 is not divisible by 11.

Option 2: 202963

• Digits at odd places (1st, 3rd, 5th from right): 3, 9, 0. Sum = \( 3 + 9 + 0 = 12 \).
• Digits at even places (2nd, 4th, 6th from right): 6, 2, 2. Sum = \( 6 + 2 + 2 = 10 \).
• Difference: \( |12 - 10| = 2 \). Since 2 is not 0 or a multiple of 11, 202963 is not divisible by 11.

Option 3: 181560

• Digits at odd places (1st, 3rd, 5th from right): 0, 5, 8. Sum = \( 0 + 5 + 8 = 13 \).
• Digits at even places (2nd, 4th, 6th from right): 6, 1, 1. Sum = \( 6 + 1 + 1 = 8 \).
• Difference: \( |13 - 8| = 5 \). Since 5 is not 0 or a multiple of 11, 181560 is not divisible by 11.

Option 4: 203456

• Digits at odd places (1st, 3rd, 5th from right): 6, 4, 0. Sum = \( 6 + 4 + 0 = 10 \).
• Digits at even places (2nd, 4th, 6th from right): 5, 3, 2. Sum = \( 5 + 3 + 2 = 10 \).
• Difference: \( |10 - 10| = 0 \). Since the difference is 0, 203456 is divisible by 11.

Conclusion

The number 203456 satisfies the divisibility rule for 11.