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