Arithmatics

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Q: If the no. ABCD, where A,B,C and D are the thousand, Hundred, tens and Unit digit, is
subtracted from DCBA. What could be the largest value?
1: 8640
2: 8840
3: 8642
4: 9999
5: 8888

I can' remember the exact values but all the choices are above 8500

[cans]

9900 - 99 = 9801

[leumas]

9900 - 99 = 9801

We need to subtract ABCD from DCBA. You've done the other way around.

[leumas]

9900 - 99 = 9801

We need to subtract ABCD from DCBA. You've done the other way around.

[[email protected]]

9900 - 99 = 9801

We need to subtract ABCD from DCBA. You've done the other way around.

I THINK WE CANT DO 9900 -99 . BECAUSE IN THAT CASE THE DCBA WILL BE 0099. BUT DCBA IS A FOUR DIGIT NO BUT 99 IS A TWO DIGIT NO
0099 IS NOT A FOUR DIGIT NO.

HELP ME HELP ME

[Brian@VeritasPrep]

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