Question

Find a $4$-digit odd number using the digits $1,2,4$ and $5$ only once such that when the first and last digits are interchanged, it is divisible by $4$.

Answer 1

Finding the required number:

A number is divisible by $4$, when the last two digits of the number is divisible by $4$.

Therefore, from the given digits, $1,2,4$ and $5$,

The last two digits which can be formed to make a number is divisible by $4$ is either $12$ or $24$.

Lets take last two digits for our number is $24$

Now, from the remaining digits, the first two digits of the number is either $15$ or $51$.

Lets take our first two digits for our number is $51$.

Therefore, the $4$ digit number which is divisible by $4$ is $5124$.

On interchanging the first and last digits of $5124$, we get the required number.

Therefore, the required $4$-digit odd number, such that when the first and last digits are interchanged, it is divisible by $4$ is $4125$.