Is r between s and t?
(1) |r -s| < |r - t|
(2) |r -s| > |s - t|
The solution already mentioned is a very novel one, it uses the basic definition of Modulus
|a| = distance of point a from Origin that is (0) or (0,0) or (0,0,0) where a can be anything rational, irrational, real or even imaginary.
and some times we spend lots of time in solving the questions algebraically, simplifying the expressions when they can be very easily done if we spend a lil more time understanding the question.
IN Most of the problems in algebra we can narrow down to the range of answer if we define the range and domain of all the functions involved in that expression.
In this example if you are not able to remember what the modulus of a number means you can always use the basic rule that
|a| < |b| implies ....... -|b| < a<|b|
apply it to both the options.