it is E...had to spend a lot of time figuring it out...took 335, 551, 553, 445, 776...atlast 776 worked

It is a step by step process,


First we have to calculate for Unit's digit B

We need a number that is B*B = B

So let us start as follows:

STEP 1

a) 0∗0=0 But entire answer will become zero

b) 1∗1=1 but the product will remain as AAB

c) 5∗5=25 but that won't be possible as (5 * A) + 2 = 7 , but we need 5

d) 6∗6=36 and 6∗A+3=5, so this value is Possible when A is 2 or A is 7

no other possible solution, so B is 6 and A is 2 or 7

STEP II

The product is AA6∗6=C656

Now if A is 2, it becomes 226∗6=1356 ; but we need C656

so if A is 7

776∗6=4656 which is = CB5B

Hence A+B+C=7+6+4=17
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