# Aptitude - Numbers - Discussion

### Discussion :: Numbers - General Questions (Q.No.18)

18.

Which one of the following numbers is exactly divisible by 11?

 [A]. 235641 [B]. 245642 [C]. 315624 [D]. 415624

Explanation:

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

 Sruthi said: (Aug 8, 2010) Can you please tell me how the sets of numbers are chosen?

 Swa said: (Aug 22, 2010) Odd places - Even places = Ans.

 Ashutosh said: (Sep 21, 2010) Tell me the method to choose the sets of numbers?

 Pradyumna said: (Oct 13, 2010) How the sets of numbers are chosen?

 Pooja said: (Oct 15, 2010) 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.

 Ali said: (Oct 15, 2010) Is this method applicable for all dividing numbers?

 Priyanka P. said: (Nov 30, 2010) @ Ali No its just for 11.. The difference b/w odd and even numbers total should be 0, 11 or multiple of 11 i.e. 22, 484 etc.

 Shoeb said: (Dec 15, 2010) Good, I like the solution. Thanks Priyanka.

 Abhishek Rana said: (Feb 25, 2011) Thanx Priyanka.

 Saranya said: (Jun 25, 2011) odd places - even places will not come because for example 4+6+1 is an odd place

 Pratiksha Sharma said: (Jun 30, 2011) 415624/11=37784. It is exactly divisible by 11. This is easiest method.

 Vimal said: (Aug 2, 2011) @ pratiksha. Ya you are right. But in aptitude test, they won't allow you to use calculator!!!

 Ish said: (Sep 13, 2011) Can any one explain it more clearly?

 Santhu said: (Sep 19, 2011) 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

 Lekha said: (Sep 24, 2011) Ple tell me how the set of numbers are chosen.

 Saurabh said: (Jan 16, 2012) What if the number is 23564?

 Arjun said: (May 14, 2012) @saurabh. 2+3+5+6+4=20 which is not exactly divisible by 11. It is exactly divisible by 2,5,10,20...

 Ramanchuchra said: (Jun 21, 2012) Can anybody tell me if sum of all digit is divisible by the no. is divisible by the whole set of numbers.

 Abhi said: (Aug 10, 2012) @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.

 Maya said: (Oct 11, 2012) 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.

 Debashish Mohapatra said: (Nov 8, 2012) 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.

 Sindhu said: (Feb 20, 2013) 2+3+5+6+4+1=21 it is not divisible by 11. 2+4+5+6+4+2=23 it is not divisible by 11. 3+1+5+6+2+4=21 it is not divisible by 11. 4+1+5+6+2+4=22 it is divisible by 11. Answer:415624.

 Masood Tahir said: (Mar 6, 2013) @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.

 Vidyadhar said: (Mar 28, 2013) Divisibility rule: Form the alternating sum of the digits. 415624 = 4-1+5-6+2-4 = 4+4-4-4 = 8-8 = 0 0 divisible by 11. So Answer is 415624.

 Bhaskar said: (Jun 19, 2013) If you take 209/11. Then your logic. Because 2+10+9=21, 21 is not divisible.

 Reena said: (Jul 9, 2013) 2+3+5+6+4+1 = 21/11. 2+4+5+6+4+2 = 25/11. 3+1+5+6+2+4 = 21/11. 4+1+5+6+2+4 = 22/11 = 2 it is divisible by 11.

 Nagasri said: (Jul 14, 2013) 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.

 Amit Chutani said: (Oct 16, 2013) 2+3+5+6+4+1 = 21/11. 2+4+5+6+4+2 = 25/11. 3+1+5+6+2+4 = 21/11. 4+1+5+6+2+4 = 22/11 = 2 it is divisible.

 Sachin said: (Aug 15, 2014) Sum of digits = (4 + 1 + 5 + 6 + 2 + 4) = 22, which must be divisible by 11. So answer is 415624.

 Suresh Venkat said: (Aug 16, 2014) @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.

 Raja Babu said: (Sep 5, 2015) 11)415624(37784 33 __ 85 77 __ 86 77 __ 92 88 __ 44 44 __ 00

 Jessy said: (Dec 30, 2016) Take the number and add all the even positions of the number and odd positions of the number then subtract those two.

 Sanjeet said: (Jan 4, 2017) What we'll do when we get odd no of digits?

 Subbu said: (May 27, 2017) 2+3+5+6+4+1=21 not divisible by 11. Calculate all given options as the same. 23 not ÷ 11. 21 not ÷ 11. 22 it is divisible by 11 so answer is D.

 Pradeep Chauhan said: (Aug 11, 2017) If sum of all digit will be divisible by 11, the answer will be correct. Ans=D 4+1+5+6+2+4=22 22 is divisible by11.

 Santosh said: (Aug 18, 2017) Nice solution, Thanks @Sindhu.

 Sasi said: (Jun 13, 2018) Is the method possible for all numbers? Please tell me.

 Akash said: (Jul 13, 2018) According to the divisible rool (sum odd places-sum of even places).

 Rekha said: (Nov 14, 2018) No, @Abhi. Because 2+0+9 = 11. Which is divisible by 11.

 Swar said: (Dec 8, 2018) To check whether a number is div by 11, it should satisfy the below condition. (sum of numbers in odd place) - (sum of numbers in even place) should be = 0 or 11 or divisible of 11.

 Muski said: (May 24, 2020) Thanks @Pooja.