Is |a - c| + |a| = |c|? (1) ab > bc (2) bc < 0

Statement 1 Alone:

We know nothing about b, so this may result in \(a > c\) or \(a < c\) depending on the sign of b.

If \(a > c > 0\), then Left side = \(2a - c\) and Right side = \(c\), equating gives \(a = c\) which is not possible. Then the statement can be answered with a "no" for this case.

If \(0 < a < c\), then we have \(c - a + a = c\) and \(c = c\), so the statement is true in this case. Since we have both "yes" and "no" cases, this statement is insufficient.

Statement 2 Alone:

b is not really our concern so this statement provides no value (we can interpret this statement as b and c have opposite signs). Insufficient.

Both Statements Combined:

If b > 0, then a > c while c < 0. Then we can have \(a > 0 > c\), plugging in the questioned equation gives \(a - c + a = -c\) and \(a = 0\), which is a possible scenario. Then this case alone already provides possible "yes" and "no" scenarios. Insufficient.

Answer: E