Need help inmath problem?

Question

in the multiplication example below ABCD and DCBA represent 4-digit numerals, and different letters represent different digits. what 4-digit number does ABCD represent?

ABCD

X9

_____

DCBA

Answer 1

OK

Let's attach it this way -

If A = 2 - for this be true, D would have to be 8 and it will not work.  You could keep going, but......

After looking at this - you will be able to quickly see that to multiply ANY 4 digit number by 9 and still end up with a 4 digit number, A MUST BE 1.

SO we have

1BC9

x9

-------

9CB1.

OK - now B, in order NOT to have any carryover would have to be 1 or smaller.  The only thing smaller than 1 (since 1 is already taken) is 0.  So B=0.

10C9

x9

------

9C01.

Now let's see -- In order to get a 0 AFTER we carry an 8, C , when multiplied by 9 must give us a "something 2".  That means C must be 8.

1089

x 9

-------

9801.

OK - that works!  

Hope that helps.