Q2. 

    (iii) From (i) and (ii) above, can you say that a number will be divisible by 11 if the difference between the  sum of digits at its odd places and that of digits at the even places is divisible by 11?

Answers (1)

Yes, 

A number will always be divisible by 11 if the difference between the sum of digits at its odd places and that of digits at the even places is divisible by 11.

So, for instance, 2728 has the alternating sum of digits 2-7+2-8 = -11. Here -11 is divisible by 11, so is 2728.

Similarly, for 31415, the alternating sum of digits is 3-1+4-1+5 = 10. This would not divisible by 11, so neither is 31415.

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