A Guide to the GRE/Absolute Value

Absolute Value The concept of absolute value - meaning a number's distance from zero - is tested on nearly every GRE. Rule Absolute 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 1. 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 Absolute 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 1. 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 =