Question

The sum of all the $4$ digited numbers that can be formed using the digits $1,2,5,6,7$ and are divisible by $2$ is

• A. $1166500$
• B. $1166400$
• C. $1166600$
• D. $1166700$

Answer 1

The correct option is A $1166500$

For number to be divisible by $2$ the last digit of the number should be either $2$ or $6$
$\because$ repetition is allowed
total number formed will be $=5\cdot 5\cdot 5\cdot 2=250$
Now at units digit $2$ and $6$ repeated $125$ times and on ${10}^{\text{th}},{100}^{\text{th}}$ and ${1000}^{\text{th}}$ each digit is repeated by $50$ times.
Hence required sum is $=50(1+2+5+6+7)(10+100+1000)+125(2+6)=1166500$