Is r between s and t? (1) |r -s| |s - t|

Question

Is r between s and t?

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

Bunuel · Accepted Answer

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.

EvaJager · Answer

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

mandyrhtdm · Answer

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.

stne · Answer

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

stne · Answer

can any body help with this query of mine, thank you

Bunuel · Answer

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?

Ravithj · Answer

1 ) In the number line,is R between S and T ? 
a.) |r-s|<|r-t| 
b.)|r-s|>|s-t|

Bunuel · Answer

Merging similar topics. Please refer to the discussion above. Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3 and 7. Thank you.

akshayk · Answer

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.

B is the answer.

AbhinavBankhwal · Answer

There can be no easier explanation than this. Thanks!

Bunuel · Answer

Similar questions: https://gmatclub.com/forum/is-s-between ... 92599.html https://gmatclub.com/forum/is-s-between ... 92600.html

Archit3110 · Answer

#1
we get |r -s| < |r - t|
t>s
s+t>2r
relation btwn r & t not know

so r....s......t or s...t....r

insufficient
#2
 |r -s| > |s - t|
2s>t+r
r>t
so we can say that
t....r....s ; sufficient
IMO B

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Is r between s and t? (1) |r -s| < |r - t| (2) |r -s| > |s - t|

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