To determine which of the numbers is divisible by 11, we can use the divisibility rule for 11. The rule states that a number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11 (including 0). Let's apply this rule step-by-step to each provided number.
a. 246542
1. Odd-positioned digits: 2, 6, 4
2. Even-positioned digits: 4, 5, 2
3. Sum of odd-positioned digits: 2 + 6 + 4 = 12
4. Sum of even-positioned digits: 4 + 5 + 2 = 11
5. Difference: |12 - 11| = 1 (1 is not a multiple of 11)
Therefore, 246542 is not divisible by 11.
b. 415624
1. Odd-positioned digits: 4, 5, 2
2. Even-positioned digits: 1, 6, 4
3. Sum of odd-positioned digits: 4 + 5 + 2 = 11
4. Sum of even-positioned digits: 1 + 6 + 4 = 11
5. Difference: |11 - 11| = 0 (0 is a multiple of 11)
Therefore, 415624 is divisible by 11.
c. 146532
1. Odd-positioned digits: 1, 6, 3
2. Even-positioned digits: 4, 5, 2
3. Sum of odd-positioned digits: 1 + 6 + 3 = 10
4. Sum of even-positioned digits: 4 + 5 + 2 = 11
5. Difference: |10 - 11| = 1 (1 is not a multiple of 11)
Therefore, 146532 is not divisible by 11.
d. 426513
1. Odd-positioned digits: 4, 6, 1
2. Even-positioned digits: 2, 5, 3
3. Sum of odd-positioned digits: 4 + 6 + 1 = 11
4. Sum of even-positioned digits: 2 + 5 + 3 = 10
5. Difference: |11 - 10| = 1 (1 is not a multiple of 11)
Therefore, 426513 is not divisible by 11.
In conclusion, the number from the provided list that is divisible by 11 is:
b. 415624
