Is r between s and t?

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Is r between s and t? [#permalink]

11 Aug 2012, 22:48

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Question Stats:

40% (02:27) correct

60% (02:09) wrong

based on 10 sessions

Is r between s and t?

(1) |r -s| < |r - t|
(2) |r -s| > |s - t|

[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Aug 2012, 06:50, edited 3 times in total.

Edited the question.

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Re: Is r between s and t? [#permalink]

12 Aug 2012, 01:21

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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.
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Re: Is r between s and t? [#permalink]

12 Aug 2012, 01:44

Bunuel wrote:

Visualizing the situation for Statement (2):
We are given that the distance between s and r is greater than the distance between s and t.

r_1---t_1--s--t_2---r_2

Now we can see that r is definitely not between s and t.
Sufficient.

Answer B
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Re: Is r between s and t? [#permalink]

12 Aug 2012, 04:04

shivanigs wrote:

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.

Re: Is r between s and t? [#permalink] 12 Aug 2012, 04:04

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Is r between s and t?

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