Process of elimination is a great approach here, since as

Economist did above, you can quite quickly rule out wrong answers here. You can also see why 9 is the correct answer if you know one elementary fact from number theory:

-to find the remainder when you divide a number by 9, you can add the digits, and find the remainder of that sum.

Because we can find remainders when dividing by 9 by adding digits (and the same works for 3), the numbers ABCDE and EDCBA must have the same remainder when we divide them by 9. That is:

ABCDE = 9q + r

EDCBA = 9k + r

So ABCDE - EDCBA = 9q + r - (9k + r) = 9(q-k)

and their difference is a multiple of 9.

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