Question

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?
A. 9
B. 6
C. 3
D. 2
E. 0

Answer 1

we need to find value of c

we have 10a +b + 10b +a = 100a + 10a +c
=> 11a + 11b = 110a +c
=>11(b -9a)=c

c is obviously, a single digit integer. this will only be possible when LHS =0 (hope you understand this part)

thus c=0

also, we see b-9a =0
=>only possibility is a=1, b=9

Answer 2

@shubhamsrg can u explain 10a+b+ 10+a part

here a wud be 1 as no 2 digits wen added will giv more than 198(99+99)
then our equ becms 1B+1B=11B
now we need to gt a no b/w 110 n 119 ( C can tak values b/w 0 to 9)
i got stuck here

Answer 3

my method indeed yielded a=1, b=9 and c=0
you can also verify

19 + 91 = 110

here, i have used the fact that AB mathematically is written as 10A+ B

eg. 76 = 10(7) + 6.

you must not be stuck here,comeon!

Answer 4

Every number comprises of :

Unit, ten, hundred part:

Like 69 = 6*10 + 9*1

So;

unknown number : ab = 10a + b