I love this question - and keep in mind that the GMAT's question creation process is pretty thorough so they'd probably do a clear and concise job of defining that both ABCD and DCBA are four-digit numbers.
If that's the case, neither A nor D can be 0. And if you're subtracting:
DCBA
-ABCD
And you want the biggest possible result, your goals are:
-You want D to be as big as possible, since it gives you 1000*D and only takes away D.
-Similarly, you want C to be as big as possible, since it gives you 100C and only takes away 10C.
-You want B, then, to be as small as possible, since you take away 100B and only add 10B.
-And you also want A to be as small as possible since you take away 1000A and only add A.
So for D to be as big as possible, that's 9, and so is C. And for B to be as small as possible, that's 0. And since you can't use 0 for A but you want it to be as small as it can possibly be, then you'd use 1. So you have:
9901
-1099
--> 8802
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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