Hi Gmatasap,

In most cases, when TESTing VALUES, you normally need just one 'set' of values and you'll find the correct answer. In tougher questions though, you'll need multiples TEST cases and sometimes you have to choose values for each individual answer (as is the case here). The 'key' is to keep the numbers small and simple (since there's no restriction about what A and B could be, then we can use positives, negatives and even 0)...

Here's how you can prove that an answer COULD be negative...

Answers A, B and C - since we're subtracting an absolute value from another absolute value, we need the 2ND absolute value to be BIGGER than the first...

Answer A:
A = -1, B = 1
|-1 + 1| - |-1 - 1| = |0| - |-2| = 0 - 2 = -2

Answer B:
A = -1, B = 1
|-1 + 1| - |-1| = |0| - |-1| = 0 - 1 = -1

Answer C:
A = 1, B = -2
|2 - 2| - |1 - -2| = |0| - |3| = 0 - 3 = -3

With two possibilities remaining (both of which look 'more complicated' than the first 3 answers), you can choose whichever looks 'easier.' Since Answer E includes CUBED terms (and we can easily make a cubed term negative), I would choose to focus on that answer...

Answer E:
A = 0, B = -2
0^3 + (-2)^3 - 0 - (-2) = 0 - 8 + 0 + 2 = -6

We've proven that 4 of the 5 answers COULD be negative, so the remaining answer must be the correct one.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich