Is |a| = b - c ?

Is \(|a|=b-c\) true? Now, if \(a\geq{0}\), the question becomes "is \(a=b-c\) true?" and if \(a\leq{0}\), the question becomes "is \(-a=b-c\) true?".

(1) \(a+c\neq{b}\) --> \(a\neq{b-c}\), we cannot answer No to the question as we don't know whether \(a>0\). Not sufficient.

(2) \(a<0\), so the question becomes is \(-a=b-c\), but we don't know that. Not sufficient.

(1)+(2) From: \(a\neq{b-c}\) and \(a<0\) we can not determine whether \(-a=b-c\) is true. For example if \(a=-1\), \(b=1\) and \(c=0\) then answer to the question will be YES but if \(a=-1\), \(b=1\) and \(c=1\) then answer to the question will be NO. Not sufficient.

Answer: E.


I think that there might be a typo in statement (2) and it should read \(a>0\) (instead of \(a<0\)), then for (1)+(2) we would have: as from (2) \(a>0\) then the question becomes "is \(a=b-c\) true?" and (1) (\(a\neq{b-c}\)) directly gives us the answer NO. In this case answer would indeed be C.

Hope it's clear.