a given number is divisible by 11 , if the difference between the sum of the digits at odd places and the sum of the digits at even places (from the right ) is either 0 are divisible by 11
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Tests for Divisibility
A number is divisible by 11...
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A number is divisible by 11 if the difference of sums of even and odd places is "0" or a multiple of 11
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If the difference of the sum of alternative digits of a number is divisible by 11 then that number is divisible by 11.
In order to check whether a number like 2143 is divisible by 11 following is the procedure.
Group the alternative digits i.e. digits which are in odd places together and digits in even places together. Here, 24 and 13 are two groups.
Take the sum of the digits of each group i.e. 2+4=6 and 1+3=4
Now find the difference of the sums; 6−4=2
If the difference is divisible by 11, then the original number is also divisible by 11. Here 2 is the difference which is not divisible by 11.
Therefore, 2143 is not divisible by 11.
Hence, the statement a number is divisible by 11 if the difference of sums of even and odd places is 0 or a multiple of 11 is true.
Answer:
true
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