Bunuel wrote:

Is r between s and t?

We are asked whether we have either of the following cases:

----s--r----t----

----t--r----s----

(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).

Not sufficient.

(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.

Answer: B.

small query

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

or

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 ?

Thank you

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- Stne