A Guide to the GRE/Absolute Value
Absolute Value[edit]
The concept of absolute value  meaning a number's distance from zero  is tested on nearly every GRE.
Rule[edit]
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[edit]
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 34k  2  12 = 3, what is the value of k?
Comments[edit]
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[edit]
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 34k  2  12 = 3, then
34k  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 =