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

It is currently 23 Oct 2014, 08:55

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the xy-plane, region R consists of all the points (x, y) such

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 18 Aug 2009
Posts: 437
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 6

Kudos [?]: 53 [0], given: 16

In the xy-plane, region R consists of all the points (x, y) such [#permalink] New post 01 Apr 2011, 22:01
In the xy-plane, region R consists of all the points (x, y) such that 2x + 3y <= 6. Is the point
(r, s) in region R ?
(1) 3r + 2s = 6
(2) r <= 3 and s <= 2


Can someone solve this problem graphically. I have trouble understanding the explanation given in OG.
If it is explained graphically, it would be greatly appreciated.
Thank you
_________________

Never give up,,,

3 KUDOS received
Manager
Manager
avatar
Joined: 03 Mar 2011
Posts: 94
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Followers: 1

Kudos [?]: 91 [3] , given: 12

Re: OG, question 121, please, help with the graph [#permalink] New post 02 Apr 2011, 07:27
3
This post received
KUDOS
The initial set R is y<=2-2x/3
Image


The set from (1) is line y=3-3x/2
As you could see the line has points in the set R and outside it
Image


The set from (2) is y<=2, x<=3
As you can see the blue set has points lying into the red set R and outside of it
Image

The intersection of both sets (1) and (2) together also does not give definiteness.
As you could see from the picture, the green line goes both through blue set only and through red and blue sets.
Image
SO, the answer is E.
_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

3 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2039
Followers: 128

Kudos [?]: 953 [3] , given: 376

Re: OG, question 121, please, help with the graph [#permalink] New post 02 Apr 2011, 13:52
3
This post received
KUDOS
mirzohidjon wrote:
In the xy-plane, region R consists of all the points (x, y) such that 2x + 3y <= 6. Is the point
(r, s) in region R ?
(1) 3r + 2s = 6
(2) r <= 3 and s <= 2


Can someone solve this problem graphically. I have trouble understanding the explanation given in OG.
If it is explained graphically, it would be greatly appreciated.
Thank you


Please see the attached image.

The turquoise line is the stem inequality 2x + 3y <= 6. Because the inequality says "<=", the region below the line will be valid region. Below means South-West side or the left side of the line.

(1)
It is the equation of a line that is denoted by red line.
Just look at the intersection of turquoise and red-line. It is at about (1.4,1.1). All red points above that intersection is outside the region defined by the turquoise line and all red points below that intersection is within the region. Thus, (r,s) may be within the region or outside the region.
Not Sufficient.

(2)
It is denoted by the blue lines. The point of intersection is (3,2). Thus, everything that is south-west from that point will be the region. South-west means below and left of the co-ordinate.
We can clearly see that (0,0) is within the range that is defined by the turquoise line.
And (3,2) is a point outside the region that is defined by the turquoise line.
Thus (r,s) could be within the turquoise region or outside of it.
Not Sufficient.

Combining both statements;
We still have two regions: one within the turquoise, another outside.
Outside the turquoise region: The red line between horizontal blue line and turquoise line.
Within the turquoise region: The red line between vertical blue line and turquoise line.
Not Sufficient.

Ans: "E"
Attachments

Inequality_Graphical.png
Inequality_Graphical.png [ 19.19 KiB | Viewed 2930 times ]


_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 929
Followers: 11

Kudos [?]: 200 [0], given: 123

Reviews Badge
Re: OG, question 121, please, help with the graph [#permalink] New post 02 Apr 2011, 21:45
bagrettin / fluke
By intersection of 1) +2) we are talking about this trapezium AAAA. Is this correct? Pls see the picture
Attachments

coor.jpg
coor.jpg [ 44.1 KiB | Viewed 2881 times ]

1 KUDOS received
Manager
Manager
avatar
Joined: 03 Mar 2011
Posts: 94
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Followers: 1

Kudos [?]: 91 [1] , given: 12

Re: OG, question 121, please, help with the graph [#permalink] New post 02 Apr 2011, 22:02
1
This post received
KUDOS
gmat1220
No.
As you could see the set (1) is just a green line, not any area.
The set (2) is blue infinite rectangle.
Therefore the inersection of (1) and (2) can not be anything but the part of the line or separate points.
The intersection of (1) and (2) is a part of green line, which goes through blue set, between the points of intersection of the green line and two blue lines: vertical and horizontal.
_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

1 KUDOS received
Manager
Manager
User avatar
Joined: 19 Apr 2009
Posts: 178
Location: San Francisco, California
Followers: 50

Kudos [?]: 180 [1] , given: 1

Re: OG, question 121, please, help with the graph [#permalink] New post 28 Jun 2011, 11:14
1
This post received
KUDOS
Here is a video explanation to this problem: http://www.gmatquantum.com/list-of-vide ... ds121.html
This is a really difficult problem, but I do recommend students to learn the pieces in this problem that are likely to be relevant to new GMAT questions.
_________________

Free Video Explanations: OFFICIAL GUIDE GMAT 13, 12, 11, 10; QUANT REVIEW 2nd, 1st.

Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 557
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 64

Kudos [?]: 288 [0], given: 11

Re: In the xy-plane, Region R consists of [#permalink] New post 02 Aug 2011, 20:19
Solution for the changed problem:

Using statement (1), if 3r + 2s=6, then at (2,0) the point (r,s) lies within region R but at (0,3) it does not. Insufficient.

Using statement (2), if r<=3 and s<=2, then the point (0,2) lies within the region R but the point (3,2) does not. Insufficient.

Combining statements (1) and (2), the point (2,0) lies within region R and satisfies both the statements too. However, the point (1,3/2) does not lie within the region R even though it satisfies both the other statements. Insufficient.

Therefore (E) is the answer.
_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

Get a free detailed MBA profile evaluation

Top MBA Rankings and MBA Admissions blog


Image

Intern
Intern
avatar
Joined: 23 Apr 2011
Posts: 1
Schools: HBS '14
Followers: 0

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

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink] New post 09 Nov 2011, 19:59
how are you supposed to do this question in 1-2 minutes? or can we give ourselves more time for difficult questions like these? if one anticipates scoring highly on the quant section does it mean every question is going to be hard? (and hence every question will be this difficult, and thus can't take more than avg for every question?)
Manager
Manager
avatar
Joined: 20 Oct 2011
Posts: 123
Location: Canada
Concentration: Sustainability, General Management
GMAT 1: 710 Q49 V38
GPA: 3.98
Followers: 1

Kudos [?]: 13 [0], given: 11

Re: In the xy-plane, region R consists of all the points (x, y) [#permalink] New post 14 Nov 2011, 08:55
This question is rather difficult and I know that I would struggle to do it under 2 minutes. However, if you can get sketch the graph relatively quickly and see what they are asking by sketching the 2 conditions, it is doable.

OG's explanation is not as intuitive and I would have a difficult time using that method to solve this in 2 minutes.
Re: In the xy-plane, region R consists of all the points (x, y)   [#permalink] 14 Nov 2011, 08:55
    Similar topics Author Replies Last post
Similar
Topics:
In the xy-plane, region R consists of all the points (x,y) thanatoz 1 23 Apr 2010, 03:05
In the xy-plane, region R consists of all the points (x,y) sam76 6 26 Feb 2008, 16:30
In the xy-plane, region R consists of all the points (x, y) gluon 4 23 Sep 2007, 07:48
In the xy-plane, region R consists of all the points (x, y) johnycute 7 20 Dec 2006, 06:05
In the xy-plane, region R consists of all the points (x.y) DLMD 15 15 Feb 2005, 23:22
Display posts from previous: Sort by

In the xy-plane, region R consists of all the points (x, y) such

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.