|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 06 Aug 2006
Posts: 21
Followers: 0
Kudos [?]:
2
[1] , given: 2
|
In the rectangular coordinate system shown above, which [#permalink]
 10 Feb 2010, 13:06
1
This post received
KUDOS
Question Stats:
57% (02:16) correct
42% (00:47) wrong based on 9 sessions
In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here) A. None B. Ι C. ΙI D. ΙII E. IV
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11519
Followers: 1795
Kudos [?]:
9546
[4] , given: 826
|
Re: GMAT Paper test - Test Code 14 [#permalink]
10 Feb 2010, 13:31
4
This post received
KUDOS
loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. {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. Answer: E.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 06 Aug 2006
Posts: 21
Followers: 0
Kudos [?]:
2
[0], given: 2
|
Re: GMAT Paper test - Test Code 14 [#permalink]
10 Feb 2010, 13:52
Bunuel wrote: loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. {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. Answer: E. Thats great! I understand it now. I always seem to have problems with co-ordinate geometry. The official answer is E.
|
|
|
|
|
|
Intern
Joined: 30 Mar 2010
Posts: 1
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: GMAT Paper test - Test Code 14 [#permalink]
30 Apr 2010, 22:24
loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. Let us represent the equation in the intercept form: x/a + y/b = 1 x/(-3) + y/(2) >= 1 Now plot these intercepts on the chart and you will find that the quadrant not being touched is IV.
|
|
|
|
|
|
Manager
Joined: 29 Oct 2011
Posts: 157
Concentration: General Management, Technology
GMAT 1: 760 Q49 V44
GPA: 3.76
Followers: 1
Kudos [?]:
43
[3] , given: 14
|
Re: GMAT Paper test - Test Code 14 [#permalink]
03 Nov 2011, 07:41
3
This post received
KUDOS
Here's my approach, which i think is easiest. Draw the equation line by determining to points, the easiest points are (0,y) and (x,0). Those points are (-3,0) and (0,2). Draw the line through the 2 points. Now pick one point and see if the inequality should be shaded to the left or to the right. I picked (-3,0), the inequality states that x<=-3, so shade to the left. you'll clearly see that the only quadrant that has no shading is IV.
_________________
Giving +1 kudos is a better way of saying 'Thank You'.
|
|
|
|
|
|
Senior Manager
Joined: 29 Jan 2011
Posts: 401
Followers: 0
Kudos [?]:
8
[0], given: 87
|
Re: GMAT Paper test - Test Code 14 [#permalink]
20 Nov 2011, 16:38
loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. Hello can someone please tell me whats wrong with this approach ? y >= -2/3 x + 6 Thus slope is negative lets find x-intercept ... substitute y=0 we get , x <= 9 . To find y-intercept substitute x=0, we get y >=6 Thus it should be 3rd quadrant... but this is wrong ...
|
|
|
|
|
|
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8
Kudos [?]:
63
[0], given: 212
|
Rectangular Coordinate System [#permalink]
20 May 2012, 03:45
In a rectangular coordinat system which quadrant, if any, contains no point (x,y) that satifies the inequality 2x - 3y <= -6? A) None B) 1st C) 2nd D)3rd E) 4th How to solve this guys any idea?
_________________
Best Regards,
E.
MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 
|
|
|
|
|
|
Manager
Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 215
Location: New Delhi, India
Followers: 2
Kudos [?]:
9
[1] , given: 12
|
Re: Rectangular Coordinate System [#permalink]
20 May 2012, 04:02
1
This post received
KUDOS
enigma123 wrote: In a rectangular coordinat system which quadrant, if any, contains no point (x,y) that satifies the inequality
2x - 3y <= -6?
A) None
B) 1st
C) 2nd
D)3rd
E) 4th
How to solve this guys any idea? 2x - 3y <= -6 => -2x + 3y >= 6 ---- (1) equate the both sides of the inequality: -2x + 3y = 6 =>x/(-3) + y/2 = 1 comparing with x/a + y/b = 1 x intercept is -3 and y intercept is 2 ie the line passes thru (-3,0) and (0,2) This line obviously passes through the 1st, 2nd and 3rd quadrant and going back to the original inequality (1) we understand the points that satisfy this inequality would be above this line which means there is no chance that any of these points would lie in quadrant 4. So the ans is E
_________________
Best
Vaibhav
If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11519
Followers: 1795
Kudos [?]:
9546
[0], given: 826
|
Re: Rectangular Coordinate System [#permalink]
20 May 2012, 12:14
|
|
|
|
|
|
Intern
Joined: 18 Apr 2011
Posts: 27
Followers: 0
Kudos [?]:
0
[0], given: 20
|
Re: In the rectangular coordinate system shown above, which [#permalink]
24 Sep 2012, 07:56
Any other way to solve this problem without plotting a graph considering that people get on average 2 mins per problem?
|
|
|
|
|
|
Senior Manager
Joined: 13 Aug 2012
Posts: 468
Followers: 12
Kudos [?]:
74
[1] , given: 11
|
Re: In the rectangular coordinate system shown above, which [#permalink]
05 Jan 2013, 02:14
1
This post received
KUDOS
loki wrote: In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
A. None
B. Ι
C. ΙI
D. ΙII
E. IV Try I: 2(1) - 3(10) = -28 Yes! Try II: 2(-10) - 3(1) = -17 Yes! Try III: 2(-10) - 3(-1) = -17 Yes! Try IV: Since y is negative and x is positive... 2x will always be positive and -3y will always be positive = No! Answer: E
|
|
|
|
|
|
|
Re: In the rectangular coordinate system shown above, which
[#permalink]
05 Jan 2013, 02:14
|
|
|
|
|
|
|
|
|
|
|
close
