Hi,
Even I believe the answer is E
If statement(2) had been a>0, then C would have been correct.

If |a|= b-c it can either be
a = b-c if a>0 or -a = b-c if a<0 or b=c if a=0
Info 1 says c+a !=b so that rules out the a>0 option
then |a| = b-c => -a = b-c if only we know a<0 and a!=0 which is given in\
the second option so the answer is C.

PS: If a=0 we can never say a=b-c and we will not have a unique answer.

srikanthb.69 wrote:If |a|= b-c it can either be
a = b-c if a>0 or -a = b-c if a<0 or b=c if a=0
Info 1 says c+a !=b so that rules out the a>0 option
then |a| = b-c => -a = b-c if only we know a<0 and a!=0 which is given in\
the second option so the answer is C.

PS: If a=0 we can never say a=b-c and we will not have a unique answer.

Hi,
You have taken |a| = b-c for granted when we have to check whether the equality holds.
I will give a counter example to disprove this :
1.)Consider: a =-1, b =2, c=1
i)a+c = 0 != b
ii)a < 0
|a| = 1, b-c =1
Is |a| = b-c? Yes
2)Consider: a =-1, b =4, c=2
i)a+c = 1 != b
ii)a < 0
|a| = 1, b-c = 2
Is |a| = b-c? No