Q37.AB+BA=AACInthecorrectlyworkedadditionproblemshown,wherethesumofthetwo-digitpositiveintegersABandBAisthethree-digitintegerAAC,andA,B,andCaredifferentdigits,whatistheunitsdigitoftheintegerAAC?96320answerE

Question

Q37.
AB
+ BA
=AAC
In the correctly worked addition problem shown,where
the sum of the two-digit positive integers AB and BA is
the three-digit integer AAC,and A,B,and C are different digits,what is the units digit of the integer AAC?
9
6
3
2
0
answer E

Answer 1

如题意,A,B为正整数,AB+BA=AAC成立,A,B,C互不相等.
因 AB+BA >= 100,但 AB+BA 不可能大于等于 200,
所以 A = 1
因 A + B >=10,所以 B =9
则 19＋91 ＝ 110 亦即 C ＝ 0