Data Sufficiency

any way to solve this problems using place value of numbers (100A + 10B + C = ABC)? im using that framework for this kind of problems. it usually works but for some reason cant figure it out for this one..

If A , B , and C are digits and AB does not = 0, what is the value of B?

(1) AB + BA = AAC

(2) A = 1

A) 1 is sufficient
B) 2 is sufficient
C) Both 1 and 2 sufficient together
D) 1 and 2 sufficient individually
E) not sufficient

topspin360 wrote:any way to solve this problems using place value of numbers (100A + 10B + C = ABC)? im using that framework for this kind of problems. it usually works but for some reason cant figure it out for this one..

If A , B , and C are digits and AB does not = 0, what is the value of B?

(1) AB + BA = AAC

(2) A = 1

A) 1 is sufficient
B) 2 is sufficient
C) Both 1 and 2 sufficient together
D) 1 and 2 sufficient individually
E) not sufficient

Of course, you can still use this framework.

Statement 1:
First off, since adding two digits is giving a 3 digit number A has to be 1( the only possible carry over digit). We can dismiss statement 2 right here as it doesn't add anything different. As A=1,
AB = 10*1 + B
BA = 10B + 1
AAC = 100+10+C = 110 + C
AB+BA = AAC

Now using the framework : AB + BA = 11 + 11B = 110 + C
=> 11B = 99 + C
=> B = 9 + C/11.
Since B is an integer and C is less than 11, C must be 0.
Then B = 9.
Sufficient.

2) is insufficient as I said earlier
A is correct