A Guide to the GRE/Absolute Value
Absolute Value
editThe concept of absolute value - meaning a number's distance from zero - is tested on nearly every GRE.
Rule
editAbsolute value makes a negative positive, but otherwise does nothing.
“| |” designates absolute value. For example, if | x + 3 | = 5, there are two possible values for x:
- x + 3 = 5, meaning x is 2
- x + 3 = -5, meaning x is -8
On an absolute value questions, split the value into two equations as seen above.
Practice
edit1. If | 3x - 4 | = 5, then what could be the value of x?
2. If | a | > a, then what is the greatest integer that a could be?
3. If 3|4k - 2| - 12 = -3, what is the value of k?
Comments
editAbsolute value tends to be tested in the quantity comparison section of the test, often with a variable modified by a constant within the absolute value. (e.g. | q + 7 | = 5) Solve these by writing out both of the potential values for the variable, and remember that either one could be the value. For example, in the prior equation, q could equal either -2 or -12, so it is unclear whether it is greater or less than -5.
Answers to Practice Questions
edit1. 3,
If | 3x - 4 | = 5 then
3x - 4 = 5
- or
3x - 4 = -5
3x - 4 = 5
- Take the first equation and solve it. First, add 4 to both sides.
3x = 9
- Now divide both sides by 3.
x = 3
- x is equal to 3. But remember, this is just one solution - you still need to solve the other equation.
3x - 4 = -5
- Now take the second equation and solve it. Add 4 to both sides.
3x = -1
- Now divide both sides by 3.
x =
- x is equal to negative one third.
This means that x = 3 or
2. -1
Absolute value makes a positive negative, but otherwise does nothing - if the absolute value of a number is greater than that number itself, the number must be negative. The greatest negative number is -1.
3. k = 5/4,
If 3|4k - 2| - 12 = -3, then
3|4k - 2| = 9
- Add 12 to both sides.
|4k - 2| = 3
- Divide both sides by 3.
4k - 2 = 3
Split both possibilities.
4k - 2 = -3
- Add 2 to to both sides
4k = 5 .
- Divide both sides by 5.
k =