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# Is r between s and t?

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Manager
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Is r between s and t? [#permalink]

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11 Aug 2012, 21:48
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Question Stats:

44% (01:29) correct 56% (01:53) wrong based on 216 sessions

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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, 05:50, edited 3 times in total.
Edited the question.

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

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12 Aug 2012, 00:21
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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.

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.

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

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12 Aug 2012, 00:44
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.

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.

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.

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

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12 Aug 2012, 03:04
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.

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

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19 Sep 2013, 00:47
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.

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.

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

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20 Sep 2013, 01:29
can any body help with this query of mine, thank you
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Re: Is r between s and t? [#permalink]

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20 Sep 2013, 01:47
stne wrote:
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.

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.

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

Not a good way to solve this problem.

What is the question you are trying to answer there?
When you say that r-s and s-t have the same/opposite signs, what cases you'd have?
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03 Mar 2014, 23:04
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1 ) In the number line,is R between S and T ?
a.) |r-s|<|r-t|
b.)|r-s|>|s-t|

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03 Mar 2014, 23:09
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Expert's post
Ravithj wrote:
1 ) In the number line,is R between S and T ?
a.) |r-s|<|r-t|
b.)|r-s|>|s-t|

Merging similar topics. Please refer to the discussion above.

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

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04 Aug 2017, 11:26
shivanigs wrote:
Is r between s and t?

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

Great Question on the core definition of absolute values.
s---r---t or t----r----s ?

1) |r-s| < |r-t|
Distance b/w r & s is less than the distance b/w r & t.
r--s-------t -> No
s-r------t -> Yes
Insufficient.

2) |r-s| > |s-t|
Distance between r & s is greater than the distance b/w s & t
=> r cannot be between s & t.
Sufficient.

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

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06 Aug 2017, 07:31
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.

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.

There can be no easier explanation than this. Thanks!

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Re: Is r between s and t?   [#permalink] 06 Aug 2017, 07:31
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