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# DS inequalities and Modulus

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Joined: 29 Jul 2012
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02 Sep 2012, 02:52
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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|
Veritas Prep GMAT Instructor
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Re: DS inequalities and Modulus [#permalink]

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06 Sep 2012, 21:59
Expert's post
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pnf619 wrote:

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 [ 2.75 KiB | Viewed 1574 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 [ 2.64 KiB | Viewed 1571 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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Last edited by VeritasPrepKarishma on 06 Sep 2012, 22:16, edited 1 time in total. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7130 Location: Pune, India Followers: 2140 Kudos [?]: 13706 [0], given: 222 Re: DS inequalities and Modulus [#permalink] ### Show Tags 06 Sep 2012, 22:13 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 [ 2.64 KiB | Viewed 1573 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 [ 2.6 KiB | Viewed 1572 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) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: DS inequalities and Modulus [#permalink]

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07 Sep 2012, 02:49
pnf619 wrote:

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).

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 $$t.$$

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