GRE Math : How to find absolute value
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Example Questions
Example Question #1 : How To Find Absolute Value
Quantitative Comparison:
Column A
|–3 + 4|
Column B
|–3| + |4|
Column A and B are equal
Column B is greater
Cannot be determined
Column A is greater
Column B is greater
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.
Example Question #2 : How To Find Absolute Value
Quantitative Comparison
|x – 3| = 3
Quantity A: x
Quantity B: 2
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
The relationship cannot be determined from the information given.
The relationship cannot be determined from the information given.
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.
Example Question #3 : How To Find Absolute Value
Quantitative Comparison
Quantity A: |10| – |16|
Quantity B: |1 – 5| – |3 – 6|
Quantity B is greater.
Quantity A is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
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.
Example Question #4 : How To Find Absolute Value
Quantitative Comparison
Quantity A: (|–4 + 1| + |–10|)2
Quantity B: |(–4 + 1 – 10)2|
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
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.
Example Question #3 : How To Find Absolute Value
Quantity A:
Quantity B:
The relationship cannot be determined from the information given
Quantity B is greater
The two quantities are equal
Quantity A is greater
Quantity B is greater
If 
Example Question #4 : How To Find Absolute Value
What is the absolute value of the following equation when 
(–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.
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