Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Oct 2016, 09:42

### 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

# In the rectangular coordinate system shown above, which quad

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 35274
Followers: 6636

Kudos [?]: 85541 [1] , given: 10237

### Show Tags

03 Mar 2014, 01:21
1
KUDOS
Expert's post
16
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:29) correct 40% (01:25) wrong based on 547 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:

Untitled.png [ 7.91 KiB | Viewed 4971 times ]
In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality $$2x - 3y\leq{- 6}$$ ?

(A) None
(B) I
(C) II
(D) III
(E) IV

Problem Solving
Question: 123
Category: Geometry Simple coordinate geometry
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35274
Followers: 6636

Kudos [?]: 85541 [1] , given: 10237

### Show Tags

03 Mar 2014, 01:21
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION

In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality $$2x - 3y\leq{- 6}$$ ?

(A) None
(B) I
(C) II
(D) III
(E) IV

$${2x-3y}\leq{-6}$$ --> $$y\geq{\frac{2}{3}x+2}$$. Thi inequality represents ALL points, the area, above the line $$y={\frac{2}{3}x+2}$$. If you draw this line you'll see that the mentioned area is "above" IV quadrant, does not contains any point of this quadrant.

Else you can notice that if $$x$$ is positive, $$y$$ can not be negative to satisfy the inequality $$y\geq{\frac{2}{3}x+2}$$, so you can not have positive $$x$$, negative $$y$$. But IV quadrant consists of such $$(x,y)$$ points for which $$x$$ is positive and $$y$$ negative. Thus answer must be E.

_________________
Intern
Joined: 22 Jun 2013
Posts: 45
Followers: 0

Kudos [?]: 40 [12] , given: 132

### Show Tags

04 Mar 2014, 03:07
12
KUDOS
3
This post was
BOOKMARKED

To draw the line on the Coordinate system consider the Inequality : $$2x - 3y\leq{- 6}$$ as $$2x - 3y={- 6}$$

We get points (0,2) & (-3,0 )
So the line looks some what as in the attachment.

To find out which area is covered by the graph put the Cordinate (0,0) in the original question $$2x - 3y\leq{- 6}$$

We get: $$0 \leq {-6}$$. Which is False.

So (0,0) does not lie in the area covered by the graph, Therefore the equation covers the area above the line.

Thus 4th Quadrant does not contain any point that satisfies the inequality. ( Rest 3 Quadrants will have a few points that would satisfy the inequality)

Not experienced enough to comment on the difficulty level.
Attachments

Q.png [ 21.53 KiB | Viewed 4940 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 35274
Followers: 6636

Kudos [?]: 85541 [1] , given: 10237

### Show Tags

08 Mar 2014, 11:41
1
KUDOS
Expert's post
SOLUTION

In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality $$2x - 3y\leq{- 6}$$ ?

(A) None
(B) I
(C) II
(D) III
(E) IV

$${2x-3y}\leq{-6}$$ --> $$y\geq{\frac{2}{3}x+2}$$. Thi inequality represents ALL points, the area, above the line $$y={\frac{2}{3}x+2}$$. If you draw this line you'll see that the mentioned area is "above" IV quadrant, does not contains any point of this quadrant.

Else you can notice that if $$x$$ is positive, $$y$$ can not be negative to satisfy the inequality $$y\geq{\frac{2}{3}x+2}$$, so you can not have positive $$x$$, negative $$y$$. But IV quadrant consists of such $$(x,y)$$ points for which $$x$$ is positive and $$y$$ negative. Thus answer must be E.

_________________
Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 640 [0], given: 723

### Show Tags

09 Mar 2014, 03:28
1
This post was
BOOKMARKED
Attachment:
The attachment Untitled.png is no longer available
In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality $$2x - 3y\leq{- 6}$$ ?

(A) None
(B) I
(C) II
(D) III
(E) IV

Sol: The inequality can be 2x=3y=-6 can be re-written in Y intercept form as y=2x/3 +2
Attachment:

Untitled1.png [ 11.93 KiB | Viewed 4772 times ]

Notice that the slop of the line is positive and hence it will definitely pass through Quad 1 and 3.
If the slope was negative then the line will definitely pass through Quad 2 and 4.

Now for x=0, y= 2 that means line will have to pass through Quad 2 as well.
Hence No point in Quad 4 will satisfy the given equation.
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Intern
Joined: 09 Feb 2013
Posts: 16
Followers: 0

Kudos [?]: 0 [0], given: 43

### Show Tags

18 Apr 2015, 11:53
Guys, I am still not clear with the solution. By any way can you simplify it further ?
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 350
Followers: 112

Kudos [?]: 883 [0], given: 84

### Show Tags

21 Apr 2015, 04:28
kshitij89 wrote:
Guys, I am still not clear with the solution. By any way can you simplify it further ?

Hi kshitij89 - For every point lying on the line segment $$2x - 3y =-6$$, the x and y coordinates are such that subtracting 3 times the y coordinate from 2 times the x coordinate is equal to -6. Examples are (3,4), (6,6) etc.

For any other point not lying on this line segment, this difference of 2x and 3y is either less than -6 or greater than -6.

The question asks us to find the location of points for which $$2x - 3y <= -6$$ is not true i.e. points for which the difference of 2x and 3y is not less than or equal to 6. For finding such points, we need to first plot its equivalent line segment in the X-Y coordinate system.

Let's see how we can plot the line. We need two points for plotting the line segment.We know that for all points on the X-axis, their Y coordinate is 0 and vice versa. So, putting x =0 in the equation of the line segment, we get the value of y = 2 and for y =0, we get the value of x = -3. Now, we have the x and the y - intercept for the line segment. Using this information, we can plot the line segment as shown below:

Now, we will need some test case to establish that on which side of the line the points do not satisfy the inequality $$2x - 3y <= -6$$. The best way is to test for the intersection point of X & Y axis i.e. (0, 0). If we put x =0 and y =0 in the inequality, we get $$0 <=-6$$ which is not true. So, we can say with certainty that the side of the line which contains ( 0, 0) does not satisfy the inequality.

This would mean that the area on the left side of the line segment $$2x - 3y =6$$ satisfy the inequality $$2x - 3y <= -6$$ and the area on the right side of the line segment do not satisfy the inequality. Since the question talks about such regions in terms of quadrants, we can observe that area on the left side of the line segment passes through Q- I, II & III only. So, we can say for sure that Q- IV does not contain any point that satisfy the inequality.

Hope this is clear. Let me know if you still have trouble in understanding of the solution.

Regards
Harsh
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Joined: 09 Feb 2013
Posts: 16
Followers: 0

Kudos [?]: 0 [0], given: 43

### Show Tags

21 Apr 2015, 10:52
Hi Harsh,

The explanation was crisp and clear but I am not sure if I will be able to solve similar questions with different nos.

Can you please provide examples of similar questions to further test my understanding ?

Regards
Kshitij
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7711
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 343

Kudos [?]: 2282 [0], given: 162

### Show Tags

21 Apr 2015, 19:59
Hi kshitij89,

How are your overall graphing "skills"? Are you comfortable with the basic concepts, formulas, drawing graphs, etc.? If so, then you'll probably handle the concept on Test Day just fine.

"Graphing", as a category, is relatively rare on the GMAT - you'll likely see just 1-2 graphing questions on Test Day and they will probably be considerably easier than this one.

Unless you've already mastered all of the 'big' categories (Algebra, Arithmetic, Formulas, Broader Geometry, Ratios, DS, etc.), then this nitpick category really isn't worth the extra time.

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 350
Followers: 112

Kudos [?]: 883 [0], given: 84

### Show Tags

21 Apr 2015, 22:43
Expert's post
1
This post was
BOOKMARKED
kshitij89 wrote:
Hi Harsh,

The explanation was crisp and clear but I am not sure if I will be able to solve similar questions with different nos.

Can you please provide examples of similar questions to further test my understanding ?

Regards
Kshitij

Hi kshitij89 - what you need is more practice to get yourself comfortable with the graphical method of solving inequalities. To begin with, I would suggest you to plot lines on the X-Y coordinate system and find out points which lie on either side of the line. You may further extend this exercise to plotting of 2 lines in the X-Y coordinate system and finding points which satisfy corresponding inequalities of both the lines.

Once you get used to it, you will prefer using the graphical method for solving inequalities. Getting comfortable with the X-Y coordinate system will also strengthen your understanding of the Coordinate Geometry section

For your practice, you may refer the following posts which uses graphical method for solving questions on inequalities and coordinate geometry:

in-the-xy-plane-region-r-consists-of-all-the-points-x-y-102233.html
in-the-xy-plane-region-a-consists-of-all-the-points-x-y-154784.html?hilit=inequalities%20inequalities%20graph
point-x-y-is-a-point-within-the-triangle-what-is-the-139419.html
set-t-consists-of-all-points-x-y-such-that-x-2-y-2-1-if-15626.html
in-the-coordinate-plane-rectangular-region-r-has-vertices-a-104869.html

Hope it helps!

Regards
Harsh
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Director
Joined: 10 Mar 2013
Posts: 608
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 11

Kudos [?]: 212 [0], given: 200

### Show Tags

17 Jul 2015, 02:26
1. Rewrite the equation (Y=mx+b) --> y=>2/3*x+2
2. Set x=0 and then y=0 --> (0, =>2); (-3<=, 0) so we have now two points the coordinate plane
3. Draw the line (see attachment) --Y you can see that Quadrant IV is not involved there (E)
Attachments

PS123.jpg [ 9.21 KiB | Viewed 2429 times ]

_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

SVP
Joined: 17 Jul 2014
Posts: 1846
Location: United States
Schools: Stanford '19
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.56
WE: General Management (Transportation)
Followers: 15

Kudos [?]: 216 [0], given: 114

### Show Tags

30 Dec 2015, 20:48
we have a positive slope and a 3 as y- coordinate when x=0.

well, regardless of what x is, line will never pass through IV, since the line must go up, and there is no way for the line to pass through IV, since it will imply that the slope is negative.
Re: In the rectangular coordinate system shown above, which quad   [#permalink] 30 Dec 2015, 20:48
Similar topics Replies Last post
Similar
Topics:
1 In the rectangular quadrant system shown above, which quadrant, if any 1 28 Aug 2016, 10:43
2 In the rectangular quadrant system shown above, which quadrant, if any 5 08 Aug 2016, 09:15
3 In the rectangular coordinate system shown above, points O, P, and Q r 3 23 Jun 2016, 12:15
13 In the rectangular coordinate system above, for which of the 12 22 Nov 2010, 06:29
62 In the rectangular coordinate system shown above, which 14 10 Feb 2010, 13:06
Display posts from previous: Sort by