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

Redeem

XY plane and R point

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Master | Next Rank: 500 Posts
Posts: 385
Joined: Fri Sep 23, 2011 9:02 pm
Thanked: 62 times
Followed by:6 members

by user123321 » Tue Nov 22, 2011 2:40 pm
karthikpandian19 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 & s<=2
IMO E
1) two lines are clearly non parallel lines(first line being a region to be exact). hence we cannot comment whether (r,s) is in region R or not.
2) if r,s is -ve then it will be in the region R
if r = 3 and s = 2 then it will be not in the region R
hence insufficient.

using both you can have r=2,s=3 outside the region R
and r=2,s=0 inside the region R
hence both are insufficient

user123321
Just started my preparation :D
Want to do it right the first time.
Top
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Tue Nov 22, 2011 4:17 pm
interesting q.
slope of function 2x+3y<=6 may be derived from y<=(2/3)x+2
slope of function 3r+2s=6 in st(1) could be derived from s=(3/2)r+2. Since two lines are not parallel (slopes are different) there should be some cross point (at least one point) which may be (r,s). However this is only one point and other points may not be in the region required. Not Sufficient.
r<=3 & s<=2 in st(2) suggests if we supply our data into y<=(2/3)x+2 and equate x with r=3, then y equated with s=4. However we are given s<=2 and again our slopes will be different here. The point (r,s) may or may not be in the region required.
Combined st(1&2) two sets of properties of linear functions with varying slopes will be Not Sufficient

e
karthikpandian19 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 & s<=2
Success doesn't come overnight!
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

=

by GMATGuruNY » Tue Nov 22, 2011 6:12 pm
karthikpandian19 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 & s<=2
Region R is composed of all the points on or below y=(-2/3)x + 2.

Statement 1: s = (-3/2)r + 3.
Image
The figure above shows that some points on s=(-3/2)r + 3 lie BELOW y=(-2/3)x + 2, while others lie ABOVE y=(-2/3)x + 2.
INSUFFICIENT.

Statement 2: r≤3 and s≤2.
Image
Inside the green box are points such that r≤3 and s≤2.
Some of the points inside the green box lie BELOW y=(-2/3)x + 2, while others lie ABOVE y=(-2/3)x + 2.
INSUFFICIENT.

Statements 1 and 2 combined:
Image
Inside the green box are points on s=(-3/2)r + 3 such that r≤3 and s≤2.
Some of these points lie BELOW y=(-2/3)x + 2, while others lie ABOVE y=(-2/3)x + 2.
INSUFFICIENT.

The correct answer is E.
Last edited by GMATGuruNY on Fri Apr 05, 2013 1:49 am, edited 2 times in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Legendary Member
Posts: 1665
Joined: Thu Nov 03, 2011 7:04 pm
Thanked: 165 times
Followed by:70 members

by karthikpandian19 » Tue Nov 22, 2011 10:43 pm
I can now understand this with pictorial rep.

Thank you very much
GMATGuruNY wrote:
karthikpandian19 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 & s<=2
Region R comprises all the points on or below y=(-2/3) + 2.

Statement 1: s = (-3/2)r + 3.
Image
The figure above shows that some points on s=(-3/2)r + 3 lie BELOW y=(-2/3)r + 2, while others lie ABOVE y=(-2/3)r + 2.
INSUFFICIENT.

Statement 2: r≤3 and s≤2.
Image
Inside the green box are points such that r≤3 and s≤2.
Some of the points inside the green box lie BELOW y=(-2/3)r + 2, while others lie ABOVE y=(-2/3)r + 2.
INSUFFICIENT.

Statements 1 and 2 combined:
Image
Inside the green box are points on s=(-3/2)r + 3.
Some of these points lie BELOW y=(-2/3)r + 2, while others lie ABOVE y=(-2/3)r + 2.
INSUFFICIENT.

The correct answer is E.
Top
User avatar
Legendary Member
Posts: 934
Joined: Tue Nov 09, 2010 5:16 am
Location: AAMCHI MUMBAI LOCAL
Thanked: 63 times
Followed by:14 members

by [email protected] » Fri Mar 16, 2012 6:29 am
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 & s<=2


The thing is could we solve the combined 1 and 2 statements without the diagrams as in the exam you cannot have the time of drawing the diagrams...
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
Top
User avatar
Legendary Member
Posts: 934
Joined: Tue Nov 09, 2010 5:16 am
Location: AAMCHI MUMBAI LOCAL
Thanked: 63 times
Followed by:14 members

by [email protected] » Mon Apr 30, 2012 2:09 am
I only have one question here, GMATguru... At the face of it when you solve this question and you come to C i.e Are both the statements sufficed or no??? then this is the point that I found...

There are two points that can be sufficed are (2,0) and (0,3).

These are the two points that is going with both the equations 2x + 3y = 6 and r<= 3 and s <= 2

And therefore (0,3) will not hold and (2,0) is the only point of (r,s).


Are there any more points that suffice both the equations.

Basically I searched for the points that go in both the equations and then does that point suffice for the main equation given in the main question...


Help needed guyzzzz....
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Mon Apr 30, 2012 2:52 am
(1) 3r + 2s = 6 may or may not lie in region R. So, (1) is NOT SUFFICIENT to answer the question.

(2) If we take r = 3 and s = 2, then the point (3, 2) does not lie in region R.
r ≤ 3 and s ≤ 2 implies we can also take negative values for r and s. If r = -2, s = -3, then (-2, -3) lies in region R.
We don't get a unique answer, so (2) is NOT SUFFICIENT to answer the question.

Combining (1) and (2), if r = 2, s = 0 then (2, 0) lies in region R. But if r = 2/3 and s = 2 then (2/3, 2) lies above the line 2x + 3y = 6, which means (2/3, 2) does not lie in region R. Combining also doesn't give a unique answer.

The correct answer is E.

Image
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Legendary Member
Posts: 581
Joined: Sun Apr 03, 2011 7:53 am
Thanked: 52 times
Followed by:5 members

by killer1387 » Mon Apr 30, 2012 3:34 am
[email protected] wrote:I only have one question here, GMATguru... At the face of it when you solve this question and you come to C i.e Are both the statements sufficed or no??? then this is the point that I found...

There are two points that can be sufficed are (2,0) and (0,3).

These are the two points that is going with both the equations 2x + 3y = 6 and r<= 3 and s <= 2

And therefore (0,3) will not hold and (2,0) is the only point of (r,s).


Are there any more points that suffice both the equations.

Basically I searched for the points that go in both the equations and then does that point suffice for the main equation given in the main question...


Help needed guyzzzz....
there are infinite number of points (as nowhere its mentioned the points are integral). Also graphically you can solve this question very easily and under less time.

Hope this helps..!!
Top
User avatar
Legendary Member
Posts: 626
Joined: Fri Dec 23, 2011 2:50 am
Location: Ahmedabad
Thanked: 31 times
Followed by:10 members

by ronnie1985 » Mon Apr 30, 2012 11:07 am
Use the graphical method to solve the problem

The equation of the straight in intercept form is x/a+y/b = 1 where a and b are the x and y intercepts respectively of the give straight line...

Given that x/3+y/2 <=1 Means all the point in the lower half of the line in xy plane satisfy the condition. Now check for the given conditions.

S1 r/2+s/3 = 1 crosses the line and hence some of its points are above the boundary defined in the question statement and some below. Not sufficient.

S2 r<=3 and s<=2. The point (3,2) is outside whereas (0,0) is inside the given boundary.

Not Sufficient

Comb.

Check in the coordinate plane for points outside the boundary. (2/3, 2) lies outside it.

Hence (E)
Follow your passion, Success as perceived by others shall follow you
Top
Post new topic Post Reply
• Page 1 of 1