BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Which Quadrant?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 57
Joined: Sun Jul 06, 2008 10:52 am
Thanked: 1 times
GMAT Score:640
by iikarthik » Thu Jul 08, 2010 6:28 am
In a rectangular Co-ordinate system,which Quadrant if any,contains no point (x,y) that satisfies the inequality 2x-3y<= -6?

A.I Quadrant
B.II Quadrant
C.III Quadrant
D.IV Quadrant
E.None

The OS is: [spoiler]D..I tried to substitute values from each quadrant in the equation eg: 1,1 ; 1,-1 but this didn't work.[/spoiler]
Thanks
karthik
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 392
Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members
Location: Bangalore, India
Thanked: 116 times
GMAT Score:770

by albatross86 » Thu Jul 08, 2010 6:45 am
I feel the easiest way to solve this problem is to simply plot the border line of the inequality in a rough graph.

i.e. Draw 2x - 3y = -6 on a graph. This has the intercepts (-3,0) and (0,2)

To find which direction this region is pointing to, simply test the origin (0,0)

2x - 3y would then be = 0 which is GREATER than -6, and hence does not satisfy our inequality. Thus the direction is away from the origin, or in other words are region is the half that does not contain the origin.

Please see the attached image for how to plot it. You can do it rough once you have your intercepts.

Thus, we can see that Quadrant IV does not contain any point that would satisfy our inequality.
Attachments
save(2).png
~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 516
Joined: Mon Nov 02, 2009 6:42 amFollowed by: 1 member
Location: Mumbai
Thanked: 14 times
GMAT Score:710

by ankurmit » Thu Jul 08, 2010 8:18 pm
You can convert this equation in form of a line as:

-3y<= -2x-6

3y>= 2x+6

y>= (2/3)x + 2

this line has positive slope with y intercept as 2

so this line will never pass through 4th quadrant..

got it?

Figure will be same as shown above by abhay :D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Mon Jul 05, 2010 6:08 am
Thanked: 3 times

by gmatsensei » Thu Jul 08, 2010 9:55 pm
albatross86 wrote:I feel the easiest way to solve this problem is to simply plot the border line of the inequality in a rough graph.

i.e. Draw 2x - 3y = -6 on a graph. This has the intercepts (-3,0) and (0,2)

To find which direction this region is pointing to, simply test the origin (0,0)

2x - 3y would then be = 0 which is GREATER than -6, and hence does not satisfy our inequality. Thus the direction is away from the origin, or in other words are region is the half that does not contain the origin.

Please see the attached image for how to plot it. You can do it rough once you have your intercepts.

Thus, we can see that Quadrant IV does not contain any point that would satisfy our inequality.
Fantastic work. I always recommend the 'graphical' approach for such problems. Obtaining the x and y intercepts will only take a few seconds. Using these, you can plot the line and bingo! The other upside to this method is that you won't have the nagging doubt as to whether you solved the inequality correctly :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1