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suneja
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
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
@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
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!
Every number comprises of : Unit, ten, hundred part: Like 69 = 6*10 + 9*1 So; unknown number : ab = 10a + b