Is r between s and t?
We are asked whether we have either of the following cases:
(1) |r -s| < |r - t|. This statement implies that the distance between r and s is less than the distance between r and t.
--------r--s------t---- (answer NO);
----s--r----------t---- (answer YES).
(2) |r -s | > |s - t|. This statement implies that the distance between r and s is greater than the distance between s and t. Now, if r were between s and t, then the distance between r and s would be less than the distance between s and t (ST would be the largest segment), thus r is not between s and t. Sufficient.
I am used to the general perception that if there is Mod on both sides of the equation then we have 2 cases
1) Both the sides of the equation have the same sign or 2) Both the sides have opposite signs
using the same logic here for statement 2 --> |r -s | > |s - t|.
I thought we could write this as r-s >s-t -->r+t>2s case 1
r-s>-s+t --> case 2 ( both the sides opposite signs ) which gives r>t
so if r>t then statement 2 is also satisfied , but here we have nothing about s
so I thought if r>t then statement 2 is also insufficient , as there is nothing about s. what is the flaw here?
why cannot we have r-s>-s+t and hence r>t for statement 2 ?