Bunuel wrote:

Official Solution:

Both statements are saying the exact same thing: \(|a|+|b|=0\), this to be true, both \(a\) and \(b\) must equal to zero.

Why is that? Absolute value is always non-negative - \(|\text{some expression}| \geq 0\), which means that absolute value is either zero or positive. We have that the sum of two absolute values, or the sum of two non-negative values equals to zero: \(\text{non-negative} + \text{non-negative} = 0\), obviously both must be zero this equation to hold true.

Answer: D

In other words, is this the logic? Re-arrange the statements to be:

(1) |a| + |b| = 0

(2) |b| + |a| = 0

If you add two positive values and they equal zero, then both values have to be zero