Question
In the following numbers, replace * by the smallest number to make it divisible by 11:
26*5
26*5
✓
Answer
26*5
Sum of the digits at odd places = 5 + 6 = 11
Sum of the digits at even places = * + 2
Difference = sum of odd terms - sum of even terms
= 11 - (* + 2)
= 11 - * - 2
= 9 - *
Now, (9 - *) will be divisible by 11 if * = 9.
i.e., 9 - 9 = 0
0 is divisible by 11.
$\therefore$ * = 9
Hence, the number is 2695.
Sum of the digits at odd places = 5 + 6 = 11
Sum of the digits at even places = * + 2
Difference = sum of odd terms - sum of even terms
= 11 - (* + 2)
= 11 - * - 2
= 9 - *
Now, (9 - *) will be divisible by 11 if * = 9.
i.e., 9 - 9 = 0
0 is divisible by 11.
$\therefore$ * = 9
Hence, the number is 2695.
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