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DS inequalities and Modulus

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DS inequalities and Modulus [#permalink] New post 02 Sep 2012, 02:52
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Please help to solve the following:-

Is s between r and t

a) |r-s| < |r-t|
b) |r-s| < |s-t|



Is s between r and t

a) |r-t| > |r-s|
b) |r-t| > |t-s|
Expert Post
Veritas Prep GMAT Instructor
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Joined: 16 Oct 2010
Posts: 4579
Location: Pune, India
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Kudos [?]: 4494 [0], given: 162

Re: DS inequalities and Modulus [#permalink] New post 06 Sep 2012, 21:59
Expert's post
pnf619 wrote:
Please help to solve the following:-

Is s between r and t

a) |r-s| < |r-t|
b) |r-s| < |s-t|



Use the number line to solve such questions. Don't get lost in algebra here.
If you are not comfortable with the distance approach of mods, check this post first: http://www.veritasprep.com/blog/2011/01 ... edore-did/

When you read "Is s between r and t", think of the following diagram:
Attachment:
Ques5.jpg
Ques5.jpg [ 2.75 KiB | Viewed 820 times ]


s can be in any one of the three regions - 'between r and t' or 'to the left of r' or 'to the right of t' (r and t can switch places too).
You need to find out whether s lies in the green line region.

a) |r-s| < |r-t|
This implies that distance between r and s is less than the distance between r and t. Look at the diagram below. This can happen in 2 ways. s can be to the left of r or it can be between r and t. Hence not sufficient.

Attachment:
Ques6.jpg
Ques6.jpg [ 2.64 KiB | Viewed 820 times ]


b) |r-s| < |s-t|
Distance between r and s is less than the distance between s and t. The same diagram as above can be used for this statement too. This can happen in 2 ways. s can be to the left of r or it can be between r and t. Hence not sufficient.

Since we get same two cases from both the statements, both together will not be sufficient.
Answer (E)
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Last edited by VeritasPrepKarishma on 06 Sep 2012, 22:16, edited 1 time in total.
Expert Post
Veritas Prep GMAT Instructor
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Joined: 16 Oct 2010
Posts: 4579
Location: Pune, India
Followers: 1032

Kudos [?]: 4494 [0], given: 162

Re: DS inequalities and Modulus [#permalink] New post 06 Sep 2012, 22:13
Expert's post
pnf619 wrote:
Please help to solve the following:-

If you are having trouble understanding the 'distance concept' of mods, check out this post first:


Is s between r and t

a) |r-t| > |r-s|
b) |r-t| > |t-s|


The question stem is the same so your initial thought process will be the same. Let's look at the statements.

a) |r-t| > |r-s|

Again, this is same as statement 1 above (|r-s| < |r-t|) so the diagram will also be the same with the same 2 cases. Notice that s cannot be to the right of t because distance between r and t must be less than the distance between r and s. Not sufficient.
Attachment:
Ques6.jpg
Ques6.jpg [ 2.64 KiB | Viewed 822 times ]


b) |r-t| > |t-s|
Distance between s and t is less than the distance between r and t. Look at the diagram. s can be between r and t or to the right of t. It cannot be to the left of r anymore because then the distance between s and t will become more than the distance between r and t. Since 2 cases are possible, the statement is not sufficient.
Attachment:
Ques7.jpg
Ques7.jpg [ 2.6 KiB | Viewed 821 times ]



Using both together, from statement 1, s cannot be to the right of t and from statement 2, s cannot be to the left of r. There is only one region left now - "between r and t". So s must be between r and t.

Answer (C)
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Karishma
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Director
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Re: DS inequalities and Modulus [#permalink] New post 07 Sep 2012, 02:49
pnf619 wrote:
Please help to solve the following:-

Is s between r and t

a) |r-s| < |r-t|
b) |r-s| < |s-t|



Is s between r and t

a) |r-t| > |r-s|
b) |r-t| > |t-s|



Use the property of absolute value, |a - b| is the distance between a and b, and visualization on the number line.

Q1:
(1) t- - - - s - - r - - s - - - - t
s and t can be on either side of r.
Not sufficient.
(2) t - - r - - - s - - - r - - t
Now r and t can be on either side of s.
Not sufficient.
(1) and (2): Still not sufficient, as one can see from the above situation for (1).

Answer E


Q2:
(1) t - - - s - - r - - s - - - t
s and t can be on either side of r.
Not sufficient.
(2) r - - s - - - t - - - s - - r
Now r and s can be on either side of t.
Not sufficient.
(1) and (2): Sufficient, because in (1) now s must be between r and t.

Answer C
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Re: DS inequalities and Modulus   [#permalink] 07 Sep 2012, 02:49
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