There are $$24$$ four digit numbers with different digits, formed by $$2,4,5$$ and $$7$$. One of these four digit numbers is a multiple of another. Which one of the following is it?

Solution

The relevant permutation is $$7425$$. It is exactly $$3$$ times $$2475$$, and $$2475$$ also uses the digits $$2,4,5,7$$ exactly once. Hence $$7425$$ is the required number.

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