Which number among 11368, 11638, 11863 and 12638 is divisible by 11?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 11638.
A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or divisible by 11.
11368:
⇒ Odd-position digits: 1, 3, 8 (sum = 1 + 3 + 8 = 12)
⇒ Even-position digits: 1, 6 (sum = 1 + 6 = 7)
⇒ Difference = 12 − 7 = 5
Since 5 is not divisible by 11, 11368 is not divisible by 11.
11638:
⇒ Odd-position digits: 1, 6, 8 (sum = 1 + 6 + 8 = 15)
⇒ Even-position digits: 1, 3 (sum = 1 + 3 = 4)
⇒ Difference = 15 − 4 = 11
Since 11 is divisible by 11, 11638 is divisible by 11.
11863:
⇒ Odd-position digits: 1, 8, 3 (sum = 1 + 8 + 3 = 12)
⇒ Even-position digits: 1, 6 (sum = 1 + 6 = 7)
⇒ Difference = 12 − 7 = 5
Since 5 is not divisible by 11, 11863 is not divisible by 11.
12638:
⇒ Odd-position digits: 1, 6, 8 (sum = 1 + 6 + 8 = 15)
⇒ Even-position digits: 2, 3 (sum = 2 + 3 = 5)
⇒ Difference = 15 − 5 = 10
Since 10 is not divisible by 11, 12638 is not divisible by 11.