|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 22 Jan 2010
Posts: 13
Followers: 0
Kudos [?]:
0
[0], given: 5
|
If ab <> 0 and points (-a,b) and (-b,a) are in the same [#permalink]
 12 Mar 2010, 15:35
Question Stats:
14% (00:00) correct
85% (01:16) wrong based on 2 sessions
1) If ab <> 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in the same quadrant?
(1) xy > 0
(2) ax > 0
2) In the xy-plane, the line k passes through the origin and through the point (a,b), where ab <> 0. Is b positive?
(1) The slope of line k is negative.
(2) a < b
|
|
|
|
|
|
|
Manager
Joined: 26 May 2005
Posts: 217
Followers: 1
Kudos [?]:
40
[0], given: 1
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
12 Mar 2010, 16:30
ahirjoy wrote: 1) If ab <> 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in the same quadrant?
(1) xy > 0
(2) ax > 0
given a!=0 and b!=0 ... a could be positive or negative and b could be positive or negative so 4 cases and the respective points mentioned ... a>0, b>0 ... points would be (-a,b) and (-b,a) and these both lie in quadrant II. GOOD a>0, b<0 ... points would be (-a,-b) and (b,a) and these both lie in different quadrants. NOT GOOD a<0, b>0 ... points would be (a,b) and (-b,-a) and these both lie in different quadrants. NOT GOOD a<0, b<0 ... points would be (a,-b) and (b,-a) and these both lie in quadrant IV. GOOD so if a>0, b>0 then the given points lie in Q II so if a<0, b<0 then the given points lie in Q IV st 1) xy>0 both x,y > 0 .. point (x,y) is in Q I both x,y < 0 .. point (x,y) is in Q IV not sufficient st 2) ax > 0 both x,a > 0 .. point (x,y) could be in Q I or QIV both x,a < 0 .. point (x,y) could be in Q II or QIII not sufficient combining a,x,y > 0 ... points would be (-a,b) and (-b,a) and these both lie in quadrant II. and point (x,y) would be in Q I a,x,y < 0 ... points would be (-a,b) and (-b,a) and these both lie in quadrant IV. and point (x,y) would be in Q III in either case, we can say (x,y) is not in the same quadrant C
|
|
|
|
|
|
Manager
Joined: 26 May 2005
Posts: 217
Followers: 1
Kudos [?]:
40
[1] , given: 1
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
12 Mar 2010, 16:34
1
This post received
KUDOS
ahirjoy wrote: 2) In the xy-plane, the line k passes through the origin and through the point (a,b), where ab <> 0. Is b positive?
(1) The slope of line k is negative.
(2) a < b
a!=0 and b!=0 .. is b>0 st 1) slope is negative .. line will be in Quadrant II(b is positive) and Quadrant IV(b is negative) not sufficient st 2) a<b this could happen in Q I, QII, Q III not sufficient combining in Q IV. a is positive and b is negative, so a is always > b .. so the point (a,b) can only be in Q II .. and b is positive C
|
|
|
|
|
|
Intern
Joined: 23 May 2010
Posts: 7
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
30 May 2010, 12:56
st 2) a<b
this could happen in Q I, QII, Q III
not sufficient
Why not a<b in Q IV? For example, a=-3 and b=-2 a< b and in Q IV...did I miss any thing? Thought answer is E
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9519
[1] , given: 826
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
30 May 2010, 13:23
1
This post received
KUDOS
tochiru wrote: st 2) a<b
this could happen in Q I, QII, Q III
not sufficient
Why not a<b in Q IV? For example, a=-3 and b=-2 a< b and in Q IV...did I miss any thing? Thought answer is E You are right: if a<b, point (a, b) can be in any quadrant. But the answer to this question is still C. In the xy-plane, the line k passes through the origin and through the point (a,b), where ab does not equal zero. Is b positive? (1) If slope is negative and the line passes through the origin, point (a,b) can be either in the II quadrant or in the IV ( a and b have opposite signs). So, b can be positive or negative. Not sufficient. (2) a<b, not sufficient by itself. (1)+(2) a<b and they have opposite signs, means b is positive (point lies in the second quadrant). Sufficient. Answer: C.
_________________
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: 23 May 2010
Posts: 7
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
30 May 2010, 20:08
Sorry..still didnt get.
How can we conclude that a and b have opp signs and hence in Q 4?
St1 tells whether q1 or Q4, but st2 dont tell anything about quadrants..no?
|
|
|
|
|
|
Manager
Joined: 30 Jun 2004
Posts: 180
Location: Singapore
Followers: 1
Kudos [?]:
9
[0], given: 5
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
31 May 2010, 04:18
Bunuel, thanks for the explanation.
|
|
|
|
|
|
Intern
Joined: 23 May 2010
Posts: 7
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
02 Jun 2010, 21:07
Please answer..
How can we conclude that a and b have opp signs (based on a<b )and hence in Q 4?
Q1 case-- (a,b) = 1,2
Q4 case-- (a,b) = -3,-2
both are valid and st2 dont tell anything about quadrants
St1 tells whether point is in q1 or Q4
I am not what i am missing here..
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9519
[0], given: 826
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
03 Jun 2010, 05:39
tochiru wrote: Please answer..
How can we conclude that a and b have opp signs (based on a<b )and hence in Q 4?
Q1 case-- (a,b) = 1,2
Q4 case-- (a,b) = -3,-2
both are valid and st2 dont tell anything about quadrants
St1 tells whether point is in q1 or Q4
I am not what i am missing here.. (1) If slope is negative and the line passes through the origin, point (a,b) can be either in the II quadrant or in the IV ( a and b have opposite signs). In II quadrant x-s are negative and y-s are positive, hence if point (a,b) is in this quadrant, b (y coordinate of the point) is positive; In IV quadrant x-s are positive and y-s are negative, hence if point (a,b) is in this quadrant, b (y coordinate of the point) is negative; The above means that x and y coordinates of the point (a,b) have opposite sign (if a positive then b negative and vise-versa). So, b can be positive or negative. Not sufficient. (2) a<b, not sufficient by itself. (1)+(2) a<b --> a is less than b, as they have opposite signs, then a must be negative and b positive (point lies in the second quadrant). Sufficient. Answer: C. The examples you provide are not valid: Q1 case-- (a,b) = 1,2 - point (a,b) is in II quadrant not in I. Q4 case-- (a,b) = -3,-2 - point (-3, -2) is in III quadrant not in IV. Proper examples would b: II quadrant: point (-3, 2); IV quadrant: point (3, -2). For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature). Hope it helps.
_________________
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
|
|
|
|
|
|
Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 271
Location: Pakistan
Concentration: Strategy, Marketing
GMAT 1: 680 Q46 V37
GMAT 2: Q V
Followers: 13
Kudos [?]:
456
[0], given: 48
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
08 Mar 2012, 13:55
Bunuel wrote: You are right: if a<b, point (a, b) can be in any quadrant. But the answer to this question is still C.
In the xy-plane, the line k passes through the origin and through the point (a,b), where ab does not equal zero. Is b positive?
(1) If slope is negative and the line passes through the origin, point (a,b) can be either in the II quadrant or in the IV (a and b have opposite signs). So, b can be positive or negative. Not sufficient.
(2) a<b, not sufficient by itself.
(1)+(2) a<b and they have opposite signs, means b is positive (point lies in the second quadrant). Sufficient.
Answer: C. i have a question: if ab is not equal to 0, then it means that a & b are either both +ve or both -ve [quadrant I or III], and that b/a=m can't be equal to 0 either. with this info, how can (a,b) be in any quadrant and not just I or III?
_________________
press +1 Kudos to appreciate posts
Download Valuable Collection of Percentage Questions (PS/DS)
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9519
[0], given: 826
|
Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
08 Mar 2012, 14:00
MBAhereIcome wrote: Bunuel wrote: You are right: if a<b, point (a, b) can be in any quadrant. But the answer to this question is still C.
In the xy-plane, the line k passes through the origin and through the point (a,b), where ab does not equal zero. Is b positive?
(1) If slope is negative and the line passes through the origin, point (a,b) can be either in the II quadrant or in the IV (a and b have opposite signs). So, b can be positive or negative. Not sufficient.
(2) a<b, not sufficient by itself.
(1)+(2) a<b and they have opposite signs, means b is positive (point lies in the second quadrant). Sufficient.
Answer: C. i have a question: if ab is not equal to 0, then it means that a & b are either both +ve or both -ve [quadrant I or III], and that b/a=m can't be equal to 0 either. with this info, how can (a,b) be in any quadrant and not just I or III? just means that neither a nor b equal zero, but we cannot say anything about their sings.
_________________
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: 08 May 2011
Posts: 6
GMAT Date: 04-28-2012
Followers: 0
Kudos [?]:
0
[0], given: 3
|
Re: If ab <> 0 and points (-a,b) and (-b,a) are in the same [#permalink]
22 Apr 2012, 19:10
... hmmm why do we need to consider line and all.. my approach:
as (-a,b) and (-b,a) are in same quad that mean -a and -b are same sigh similarly b and a are same sign. Thus a and b are either both +ve or both -ve.
from stat1 - we just know about x and y that these are either both +ve and both -ve and based on that we cant say they are in same quad as a,b
stat 2 - a and x are both +ve or both -ve but we donno about x and y relation...
combining stat 1 and stat2
x,y,a,b are all +ve or x,y,a,b are all -ve thus (x,y) and (a,b) in same quad.
|
|
|
|
|
|
Manager
Joined: 16 Mar 2010
Posts: 59
Followers: 0
Kudos [?]:
4
[0], given: 4
|
Re: If ab <> 0 and points (-a,b) and (-b,a) are in the same [#permalink]
22 Apr 2012, 19:57
Thanks khushboochhabra, that is definitely an easier way to look at the problem... For those still in doubt, drawing a quick table with possible +/- combinations will help confirm that a & b need to be the same sign.
|
|
|
|
|
|
|
Re: If ab <> 0 and points (-a,b) and (-b,a) are in the same
[#permalink]
22 Apr 2012, 19:57
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
If ab not equal to 0 and (-a,b) and (-b,a) are in the same
|
kimmyg |
2 |
10 Oct 2005, 12:13 |
|
|
|
|
If ab does not equal 0 and points (-a,b) and (-b,a) are in
|
lfox2 |
4 |
15 Oct 2006, 11:43 |
|
|
|
|
If ab not= 0 and points (-a,b) and (-b,a) are in the same
|
chanmat |
4 |
25 Nov 2006, 19:33 |
|
|
|
|
If ab <>0 and points (-a,b) and (-b,a) are in the same
|
bewakoof |
2 |
22 Jul 2007, 21:23 |
 |
6
|
 |
If ab≠0 and points (-a,b) and (-b,a) are in the same
|
yaron |
134 |
28 Aug 2005, 09:46 |
|
|
|
|
|
|
close
