Question

Which of the following is divisible by 11?
A. \[3,116,365\]
B. \[901,351\]
C. \[8,790,322\]
D.NONE OF THESE

Answer 1

Hint: Here, we are given some numbers and we are required to see which number is divisible by \[11\]. We will use the divisibility test of \[11\] which is after subtraction of the sum of the digit at an even place from the sum of the digit at odd places if we get 0, \[11\] OR MULTIPLE OF \[11\] then the number is divisible by 11\[11\]and will check which number is divisible by \[11\].
Now, check each number by the rule step by step.

FORMULA USED: Sum of the digit at odd places\[ - \]sum of the digit at even places \[ = \] 0 or divisible by \[11\]

Complete answer:
We know that,
Divisibility test of \[11\] states that the sum of the digit at even place is subtracted at odd places digit the result will be either 0 or divisible by \[11\]
Now we will test it through all options
Taking option, A

A. \[3,116,365\]
Here odd place digit is \[ = \]\[3,1,3,5,1,6,6\]
Even place digit is \[ = \] \[1,6,6\]
As we know that,
Sum of the digit at odd places \[ - \]sum of the digit at even places \[ = \]0 or divisible by \[11\]
\[\left( {3 + 1 + 3 + 5} \right) - \left( {1 + 6 + 6} \right)\]
\[ = \]\[12 - 13\]
\[ = \]\[ - 1\]
Here, the result is \[ - \]1 therefore
It is not divisible \[11\].

B. \[901,351\]
Here odd place digit is \[ = \]\[9,1,5\]
Even place digit is \[ = \]\[0,3,1\]
As we know that,
Sum of the digit at odd places \[ - \]sum of the digit at even places \[ = \]0 or divisible by 11
\[\left( {9 + 1 + 5} \right) - \left( {0 + 3 + 1} \right)\]
\[ = \] \[11\]
Here, the result is \[11\].
 So, it is divisible by \[11\].

C. \[8,790,322\]
Here odd place digit is \[ = \]\[8,9,3,2\]
Even place digit is \[ = \]\[7,0,2\]
As we know that,
Sum of the digit at odd places \[ - \]sum of the digit at even places\[ = \]0 or divisible by \[11\]
\[\left( {8 + 9 + 3 + 2} \right) - \left( {7 + 0 + 2} \right)\]
\[ = \] \[13\]
Here, the result is \[13\].
therefore, it is not divisible by \[11\]

Therefore, the correct option is B

Note: Divisibility tests are shortcut methods to identify that a number is divisible by another number without dividing it.
Whenever we face such a type of question the key concept is to go through the divisibility rule.
So, always keep in mind the divisibility rule of the number to find out the result quickly.