Question

How many given numbers are not divisible by 11?

(a) 4
(b) 7
(c) 6
(d) 5

Answer 1

Hint: First, we need the divisibility rule of 11 to get the numbers which are divisible by 11. Then, the divisibility rule of 11 says that firstly we should take the sum of alternate digits from left and then subtract it from the sum of numbers present at the even places from the left and then check if the result is divisible by 11 or not. Then, check for all the numbers with above condition we know only 0 and multiples of 11 as 11, 22, 33 and so on will be divisible by 11. Then , by using it we get the numbers divisible by 11.

Complete step-by-step answer:
In this question, we are supposed to find the numbers from the cloud given below which are divisible by 11.

Now, we need the divisibility rule of 11 to get the numbers which are divisible by 11.
So, the divisibility rule of 11 says that firstly we should take the sum of alternate digits from left and then subtract it from the sum of numbers present at the even places from the left and then check if the result is divisible by 11 or not.
Now, by using the above mentioned divisibility rule to all the numbers one by one as:
$\begin{align}
  & 17871\Rightarrow \left( 1+8+1 \right)-\left( 7+7 \right)=-4 \\
 & 1007453\Rightarrow \left( 1+0+4+3 \right)-\left( 0+7+5 \right)=-4 \\
 & 4343143\Rightarrow \left( 4+4+1+3 \right)-\left( 3+3+4 \right)=2 \\
 & 990039\Rightarrow \left( 9+0+3 \right)-\left( 9+0+9 \right)=-6 \\
 & 125144\Rightarrow \left( 1+5+4 \right)-\left( 2+1+4 \right)=3 \\
 & 888888\Rightarrow \left( 8+8+8 \right)-\left( 8+8+8 \right)=0 \\
 & 6142\Rightarrow \left( 6+1 \right)-\left( 4+2 \right)=1 \\
\end{align}$
So, all the numbers give a number as a result and now we need to check if that number is divisible by 11 or not.
Then, we know only 0 and multiples of 11 as 11, 22, 33 and so on will be divisible by 11.
Now, we can clearly see only the number 888888 gives the number as 0 which is divisible by 11 and all other numbers are not divisible by 11.
Therefore the total number of numbers which are not divisible by 11 are 6.
Hence the correct answer is option C .

Note: Now, to solve these type of the questions we can use the traditional approach also so that we will each number with 11 to reach the remainder part, if the remainder is zero then the number is divisible by 11 and if the remainder is not zero then number is not divisible. But, the above explained approach is faster to calculate as compared to the traditional one.