Question

How many four-digit numbers having distinct digits using the first five natural numbers (1 to 5) can be formed such that the numbers formed are divisible by each of the digits used in the number?

• A. 1
• B. 2
• C. 3

Answer 1

There are two cases in this situation:
If we include 5: If this number consists of the digit 5 then we would need to use at least one of the even digits between 2 and 4. In this case, the number would need to be even and also divisible by 5. For this to occur, the number should end in 0 - which is not a possibility in the given case. So 5 cannot be one of these four digits.
If we do not include 5: In this case, the number would be consisting of the digits 1,2,3 and 4. In such a case, we can easily realise that such a number cannot be a multiple of 3 since the sum of digits of the number is 10.