4x(ABCD)=DCBA what is ABCD ?

Question

12703 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-10T13:23:58

#ABCD=2178#

If #A#, #B#, #C#, #D# are digits of a #4# digit number, then we can reason as follows:

Given:

#4ABCD = DCBA#

#A# is #1# or #2#, since otherwise #4ABCD# would run to #5# digits.
#A# is even since it's the last digit of #4ABCD#, so that means it must be #2#.
#D >= 8# and hence #D=8# or #9#.
Since the last digit of #4D# is #A#, we can deduce that #D=8#.
So there are no carries into the #1000#'s and there is a carry of #3# into the #10#'s. So #4BC+3 = CB#
Hence #B# is odd and #1# or #2#, so must be #1#.
Then the last digit of #4BC+3# is #1#, so the last digit of #4BC# is #8# and #C=2# or #C=7#. Hence #C=7#

#ABCD=2178#

Answer 2 · 2017-11-10T13:41:08

If #ABCD# AND #DCBA# were intended to be 4-digit numbers (with #A, B, C, and D# representing single digits:
#color(white)("XXX")ABCD=2178#

#4xx2178=8712#

(only non-zero combination that I was able to find)

Is this what you were trying to ask for?