Question

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

Answer 1

The $4$- digit number will be an odd number if the unit place digit is an odd number (i.e $1\mathrm{or}5$)

Total such odd numbers are

$4125,4215,1245,1425,2145,2415,4251,4521,5241,5421,2451,2541.$

Also we know that any $4$ digit number is divisible by $4$ if the last two digit number is divisible by $4$.

Consider a number $4521$, if we interchange the first and last digits, the new number will be $1524$.

Here, we see that the last two digit (i.e. $24$) is divisible by $4$. So the number $1524$ is divisible by $4$.

Hence, the required $4$-digit number is $4521$