- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:

**(a)** 92 _ 389 (b) 8 _ 9484

To do :

We have to find the digits in the blank spaces so that the numbers formed are divisible by 11.

Solution :

Divisibility rule of 11:

A positive integer N is divisible by $11$ if the difference of the alternating sum of digits of N is a multiple of $11$.

(a) Let the digit in the blank space be $x$ where $0 \leq x \leq 9$.

Sum of the odd digits $= 9 + 3 + 2$

$= 14$

Sum of the even digits $= 8 + x + 9$

$= x+17$

Difference $=x+17-14$

$=x+3$

Now, $x+3$ is divisible by 11.

If $x=9, x+3=9+3=12$ which is not divisible by 11.

If $x=8, x+3=8+3=11$ which is divisible by 11.

If $x=7, x+3 = 7+3 = 10$ which is not divisible by 11 and the same is the case for any value of $x<7$.

Hence, the required digit is 8.

(b) Let the digit in the blank space be $x$ where $0 \leq x \leq 9$.

Sum of the odd digits $= 4 + 4 + x$

$= x+8$

Sum of the even digits $= 8 + 9 + 8$

$= 25$

Difference $=25-(x+8)$

$=25-8-x$

$=17-x$

Now, $17-x$ is divisible by 11.

If $x=9, 17-x=17-9=8$ which is not divisible by 11.

If $x=8, 17-x=17-8=9$ which is not divisible by 11.

If $x=7, 17-x=17-7=10$ which is not divisible by 11.

If $x=6, 17-x=17-6=11$ which is divisible by 11.

If $x=5, 17-x = 17-5 = 12$ which is not divisible by 11 and the same is the case for any value of $x<5$.

Hence, the required digit is 6.

- Related Questions & Answers
- Is the digit divisible by the previous digit of the number in JavaScript
- N digit numbers divisible by 5 formed from the M digits in C++
- Check if N is divisible by a number which is composed of the digits from the set {A, B} in Python
- Add N digits to A such that it is divisible by B after each addition?
- Finding the count of numbers divisible by a number within a range using JavaScript
- Find nth number that contains the digit k or divisible by k in C++
- Show that the following grammar is LR (1) S → A a |b A c |B c | b B a A → d B → d
- Check if any permutation of a large number is divisible by 8 in Python
- Add N digits to A such that it is divisible by B after each addition in C++?
- Count n digit numbers divisible by given number in C++
- Finding all the n digit numbers that have sum of even and odd positioned digits divisible by given numbers - JavaScript
- Check if a large number is divisible by 11 or not in java
- Check if a large number is divisible by 11 or not in C++
- Smallest number that is divisible by first n numbers in JavaScript
- Largest N digit number divisible by given three numbers in C++
- C++ Program for the Largest K digit number divisible by X?