It is currently 20 Aug 2017, 16:05

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If q, s, and t are all different numbers, is q < s < t ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Top Contributor
1 KUDOS received
Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 569

Kudos [?]: 2095 [1] , given: 220

Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
If q, s, and t are all different numbers, is q < s < t ? [#permalink]

Show Tags

New post 19 Jun 2017, 04:44
1
This post received
KUDOS
Top Contributor
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

51% (02:13) correct 49% (01:31) wrong based on 238 sessions

HideShow timer Statistics

If q, s, and t are all different numbers, is q < s < t ?

(1) t - q = |t - s| + |s - q|

(2) t > q
[Reveal] Spoiler: OA

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges


Last edited by Bunuel on 19 Jun 2017, 04:59, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 2095 [1] , given: 220

Expert Post
2 KUDOS received
Math Expert
User avatar
D
Joined: 02 Sep 2009
Posts: 40959

Kudos [?]: 118973 [2] , given: 12010

Re: If q, s, and t are all different numbers, is q < s < t ? [#permalink]

Show Tags

New post 19 Jun 2017, 05:28
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
If q, s, and t are all different numbers, is q < s < t ?

(1) t - q = |t - s| + |s - q|

Notice that the right hand side is positive (it's the sum of two absolute values, so two non-negative values, in fact, in our case two positive values, since we know that the variables are distinct). Thus the left hand side must also be positive, which means that t > q. So, we can have 3 cases for s:

a. ---s---q-------t-------
In this case \(s < q < t\):
\(t - s > 0\) and \(s - q < 0\), which would mean that \(|t - s| = t -s\) and \(|s - q| = -(s - q)\) (recall that |x| = x when x > 0 and x = -x when x <= 0).
So, \(|t - s| + |s - q| = (t -s) - (s - q) = t - 2s + q\).

So, in his case we'd have \(t - q = t - 2s + q\) or \(q=s\). But we are told that q, s, and t are all different numbers, so this case is out.

b. -------q---s---t-------
In this case \(q < s < t\):
\(t - s > 0\) and \(s - q > 0\), which would mean that \(|t - s| = t -s\) and \(|s - q| = s - q\). So, \(|t - s| + |s - q| = (t -s) + (s - q) = t - q\).

This matches the info given in the statement.

c. -------q-------t---s---
In this case \(q < t < s\):
\(t - s < 0\) and \(s - q > 0\), which would mean that \(|t - s| = t -s\) and \(|s - q| = -(s - q)\). So, \(|t - s| + |s - q| = -(t -s) + (s - q) = -t + 2s - q\).

So, in his case we'd have \(t - q = -t + 2s - q\) or \(t=s\). But we are told that q, s, and t are all different numbers, so this case is out.

Only q < s < t case is possible. Sufficient.

(2) t > q. Not sufficient.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 118973 [2] , given: 12010

Expert Post
5 KUDOS received
Manhattan GMAT Instructor
User avatar
S
Joined: 04 Dec 2015
Posts: 362

Kudos [?]: 208 [5] , given: 46

GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
Re: If q, s, and t are all different numbers, is q < s < t ? [#permalink]

Show Tags

New post 19 Jun 2017, 13:27
5
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
AbdurRakib wrote:
If q, s, and t are all different numbers, is q < s < t ?

(1) t - q = |t - s| + |s - q|

(2) t > q


With less math:

Start with statement 2. This is insufficient, since s could be greater than t, or s could be between q and t. Eliminate answers B and D.

Statement 1: When you see |x - y|, think 'distance between x and y on the number line'. That's all that means. So, this statement says that t - q is equal to the distance between t and s, plus the distance between s and q. In other words, s has to be between t and q.

Jot down some diagrams on your paper to convince yourself of that: in order for the distances to make sense, s has to be in the middle.

Image

Also, t-q has to be positive, since it's the sum of two absolute values. So, t is greater than q.

If t is greater than q and s is in the middle, you know that q < s < t. Sufficient.
_________________


Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

Did you like this post? Check out my upcoming GMAT classes and blog archive!

Suggestions for blog articles are always welcome! Please send your ideas via private message.

Manhattan Prep GMAT Discount | Manhattan Prep GMAT Reviews

Kudos [?]: 208 [5] , given: 46

Re: If q, s, and t are all different numbers, is q < s < t ?   [#permalink] 19 Jun 2017, 13:27
    Similar topics Author Replies Last post
Similar
Topics:
14 Experts publish their posts in the topic If p, q, r, and s are consecutive integers, with p < q < r < s, is pr Bunuel 7 03 Nov 2016, 06:51
16 Experts publish their posts in the topic If x < p < q < y. Is |q - x| < |q - y|? jamifahad 16 07 May 2017, 12:28
1 Experts publish their posts in the topic The positive integers are such that p < q r < s < hussi9 3 20 May 2011, 06:32
2 Experts publish their posts in the topic If p/q > 5, is q < 2? jeeteshsingh 6 15 Oct 2013, 09:14
5 Experts publish their posts in the topic If p, q and r are even numbers, and 2<p<q<r, What is the val TheRob 9 22 Jun 2017, 08:37
Display posts from previous: Sort by

If q, s, and t are all different numbers, is q < s < t ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.