Question

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

Answer 1

We know that, 4-digit number is said to be an odd number, if unit place digit is an odd number (i.e. 1 or 5).

Given digits are 1, 2, 4 and 5.

Total such odd numbers are 4125, 4215, 1245, 1425, 2145, 2415, 4251, 4521, 5241, 5421, 2451 and 2541.

Also, we know that, any 4-digit number can be divisible by 4, if the last two digits of that number is divisible by 4.
Consider a number 4521.

If we interchange the first and the last digits, then the new number = 1524.

Here, we see that the last two digits (i.e. 24), which is divisible by 4.

So, 1524 is divisible by 4.

Required 4-digit number = 4521.

There are three more numbers which is divisible by 4, such that 2415, 2451 and 4125.