It is currently 22 Jun 2017, 17:40

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

DS inequalities and Modulus

Author Message
Intern
Joined: 29 Jul 2012
Posts: 14

Show Tags

02 Sep 2012, 03:52
1
This post was
BOOKMARKED

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
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India
Re: DS inequalities and Modulus [#permalink]

Show Tags

06 Sep 2012, 22:59
Expert's post
3
This post was
BOOKMARKED
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 1633 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 1629 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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Last edited by VeritasPrepKarishma on 06 Sep 2012, 23:16, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India
Re: DS inequalities and Modulus [#permalink]

Show Tags

06 Sep 2012, 23:13
pnf619 wrote:

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 1632 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 1630 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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: DS inequalities and Modulus [#permalink]

Show Tags

07 Sep 2012, 03:49
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 \(t.\)

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Re: DS inequalities and Modulus   [#permalink] 07 Sep 2012, 03:49
Similar topics Replies Last post
Similar
Topics:
Explanation related to inequalities 2 10 Sep 2016, 19:41
Inequalities 2 15 Oct 2015, 21:36
1 Number theory and Inequalities issues 7 24 Jun 2014, 11:06
inequality 1 15 Sep 2012, 08:37
Modulus 1 26 Mar 2012, 20:59
Display posts from previous: Sort by