If , then either or must be negative, but not both. Making them both positive, as in quantity B, and then adding them, would produce a larger number than adding them first and making the result positive.

(–3)3 = –27. Any time a negative number is cubed, it remains negative. –27 + 5 = –22. The absolute value of any number will ALWAYS be positive so the absolute value of –22 is 22. This is our answer.

Quantity A: |–4 + 1| = |–3| = 3 and |–10| = 10, so (|–4 + 1| + |–10|)2 = (3 + 10)2 = 132 = 169

Quantity B: |(–4 + 1 – 10)2| = |(–13)2| = 169

The two quantities are equal.

The operations in the absolute value are always done first. So in Column A, |–3 + 4| = |1| = 1. In Column B, |–3| + |4| = 3 + 4 = 7.

It's important to remember that absolute value functions yield two equations, not just one. Here we have x – 3 = 3 AND x – 3 = –3.

Therefore x = 6 or x = 0, so the answer cannot be determined.

If we had just used the quation x – 3 = 3 and forgotten about the second equation, we would have had x = 6 as the only solution, giving us the wrong answer.

Quantity A: |10| = 10, |16| = 16, so |10| – |16| = 10 – 16 = –6.

Quantity B: |1 – 5| = 4, |3 – 6| = 3, so |1 – 5| - |3 – 6| = 4 – 3 = 1.

1 is bigger than –6, so Quantity B is greater.