Aptitude - Numbers - Discussion

To check whether a number is divisible by 11, sum the digits in the odd positions counting from the left (the first, third, ....) and then sum the remaining digits. If the difference between the two sums is divisible by 11, then so is the original number. Otherwise it is not.

Why does this work?

I have tried to work it out. My solutions are:

1) if the answer for the subtraction is 0, it is divisible.
2) if the answer for the subtraction is not 0, it is not divisible.

It is the principle for dividing any No. by 11.

If the difference between odd & even places No. comes 0 or 11 or multiple of 11 i.e. 22, 99, 121 etc. Then the whole No. will be divided by 11.

For example we also have principle for dividing any No. by 2. i.e.the unit place No. is divided by 2 that means the whole No. is divided by 2.

There is another method as well. In the option A, B, C. If you will add all the digits of the given number the result will not be divisible by 11. But if you will add the digits of the number given in option D.

i.e - 415624=4+1+5+6+2+4=22 which is divisible with 11.

This formula is also applicable for any number.

Example:
415624
Position (from right) Digit Position Type
1 4 Odd
2 2 Even
3 6 Odd
4 5 Even
5 1 Odd
6 4 Even
Odd positions: 4, 6, 1

Even positions: 2, 5, 4
sum(odd positions) − sum(even positions)

If that difference is 0 or divisible by 11, the number is divisible by 11.

Alternative numbers sum and take their difference. if the difference is 0 or divisible by 11.

Then that numbers are divisible by 11. that means,

eg:415624.

4+5+2 = 11.
1+6+4 = 11.

then difference = 11-11 = 0.

divisible by 11.

If we take any number. We got answer.

Separate the digits into odd and even positions (from right to left).
Sum the digits at odd positions and sum the digits at even positions.

Find the difference between these two sums.
If the difference is 0 or divisible by 11, then the number is divisible by 11.

@Arjun.
You are wrong.

EX- if you take 209/11.

Then your logic is wrong.

Because 2+0+9=11, and 11/11=1.

And I request you don't post wrong information because many peoples are confused with this type of example.

Hope you understand.

@Amit.

Method which you tried is entirely different.

It is not suitable for all no's. but for finding the / by 3 is correct. if (even position no sum)-(odd position no sum) = 0 or 11 then it will be divisible by 11.

By sum of all digits can be divisible by 11 also we can calculate.

1. option sum is 21 so it is not divisible with 11
2. option not
3. option not
4. option sum is 22 is divisible by 11

So ans is 4.option

@abhi.

I think Arjun is right as;

209/11= 19 which is completely devise-able by 11 by leaving no remainder, with short cut method for aptitude as; 2+0+9=11 which is also completely divided by 11.