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 →

Cartesian Problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members
Thanked: 114 times
by knight247 » Sun Aug 28, 2011 4:47 am
Which quadrants, if any, contain points on the line y = x/1000+ 1,000,000?

This is a Manhattan problem. The answer is 1,2,3

The normal way of going about this is put x=0 and u get y=10^6 then put y=0 and get x=-10^9

When u draw the points (0,10^6) and (-10^9,0),u see that the line joining them passes thru quadrant 1,2 and 3. So great.

But here is where i have a problem. I've come across two thumb rules (1) if slope is -ve then the line passes thru quadrants 1,2 and 4 and (2) if slope is positive then the line passes thru quadrants 1,3 and 4

If I rearrange the terms of y = x/1000+ 1,000,000 then I get -x+1000y=10^9. Comparing this eqn with ax+by+c, I get, a=-1 and b=1000. Slope=-a/b=-(-1)/1000=1/1000 which is positive. So as per rule (2) shouldn't this line pass thru quadrants 1,3 and 4? Opinions?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members
Location: India
Thanked: 375 times

by Frankenstein » Sun Aug 28, 2011 5:46 am
I've come across two thumb rules (1) if slope is -ve then the line passes thru quadrants 1,2 and 4 and (2) if slope is positive then the line passes thru quadrants 1,3 and 4
Hi,
You must have missed other constraints. When the slope is negative, it will definitely pass through Q2 and Q4. But, whether it passes through Q1 or Q3 depends on the constant, c(y-intercept) in y=mx+c.
If c>0, it passes through quadrants 1,2,4.
If c<0, it passes through quadrants 2,3,4.
If c=0, it passes through Q2 and Q4 only.

Similarly, you can check for positive slope.
Cheers!

Things are not what they appear to be... nor are they otherwise
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members
Location: New York City
Thanked: 130 times
GMAT Score:780

by gmatboost » Sun Aug 28, 2011 10:02 pm
What Frankenstein wrote is absolutely right, I want to add to it the reasoning, since I think it is better to learn reasoning than to memorize rules.

A line with positive slope moves up as it moves to the right, and it moves down as it moves to the left. This means that eventually, no matter how long it takes, a line with positive slope will move up-right enough to be in quadrant 1, and down-left enough to be in quadrant 3.

Imagine that this positively-sloped line goes through the origin. In this case, it only moves through Quadrants 1 and 3. (Actually visualize this, don't just read the words.)

If we shift it up just a tiny bit, it will also go through quadrant 2, but never through 4.
Conversely, if we shift it down just a tiny bit, it will also go through quadrant 4, but never through 2.

The reverse of all of this is true with a negatively-sloped line:

As it moves to the right it moves down, and it moves up as it moves to the left. This means that eventually, no matter how long it takes, a line with negative slope will move down-right enough to be in quadrant 4, and up-left enough to be in quadrant 2.

Imagine that this positively-sloped line goes through the origin. In this case, it only moves through Quadrants 2 and 4. (Actually visualize this, don't just read the words.)

If we shift it up just a tiny bit, it will also go through quadrant 1, but never through 3.
Conversely, if we shift it down just a tiny bit, it will also go through quadrant 3, but never through 1.

Hope this is helpful.
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 540
Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members
Thanked: 37 times

by navami » Mon Aug 29, 2011 12:28 pm
Put x = 0
then Y = 0
This time no looking back!!!
Navami
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 608
Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members
Thanked: 37 times

by saketk » Mon Aug 29, 2011 10:33 pm
knight247 wrote:Which quadrants, if any, contain points on the line y = x/1000+ 1,000,000?

This is a Manhattan problem. The answer is 1,2,3

The normal way of going about this is put x=0 and u get y=10^6 then put y=0 and get x=-10^9

When u draw the points (0,10^6) and (-10^9,0),u see that the line joining them passes thru quadrant 1,2 and 3. So great.

But here is where i have a problem. I've come across two thumb rules (1) if slope is -ve then the line passes thru quadrants 1,2 and 4 and (2) if slope is positive then the line passes thru quadrants 1,3 and 4

If I rearrange the terms of y = x/1000+ 1,000,000 then I get -x+1000y=10^9. Comparing this eqn with ax+by+c, I get, a=-1 and b=1000. Slope=-a/b=-(-1)/1000=1/1000 which is positive. So as per rule (2) shouldn't this line pass thru quadrants 1,3 and 4? Opinions?

Hi-- I understand that remembering theorems and rules is extremely important, but do we need to do all this in this question?

Looking at the question: isn't it obvious that if the value of X is Positive then Y can never be NEGATIVE ?

Hence, it can never belong to the 4th quadrant.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members
Location: New York City
Thanked: 130 times
GMAT Score:780

by gmatboost » Tue Aug 30, 2011 7:21 am
Yes, you can certainly look at the equation and confirm that (pos, neg) is never a possible value for (x, y). You should also double-check that each of the other three are possible (which they are).

I don't think that what I described actually takes all that long once you understand the trajectory of lines with positive slope and lines with negative slope.

But it's very helpful to think through your approach as well. This same approach is also helpful on DS questions some times. For example, if you see a - b > 0 you could conclude that it's not possible for both a < 0 and b > 0 to be true at the same time.
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 608
Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members
Thanked: 37 times

by saketk » Tue Aug 30, 2011 8:04 am
gmatboost wrote:Yes, you can certainly look at the equation and confirm that (pos, neg) is never a possible value for (x, y). You should also double-check that each of the other three are possible (which they are).

I don't think that what I described actually takes all that long once you understand the trajectory of lines with positive slope and lines with negative slope.

But it's very helpful to think through your approach as well. This same approach is also helpful on DS questions some times. For example, if you see a - b > 0 you could conclude that it's not possible for both a < 0 and b > 0 to be true at the same time.
yes, I totally agree with you.. actually I wanted knight247 to see this alternate approach as well... :)

thanks for method you described.. it helps
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1