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If ab <> 0 and points (a,b) and (b,a) are in the same [#permalink]
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12 Mar 2010, 15:35
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1) If ab <> 0 and points (a,b) and (b,a) are in the same quadrant of the xyplane, is point (x,y) in the same quadrant?
(1) xy > 0 (2) ax > 0
2) In the xyplane, 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



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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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12 Mar 2010, 16:30
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ahirjoy wrote: 1) If ab <> 0 and points (a,b) and (b,a) are in the same quadrant of the xyplane, 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



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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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12 Mar 2010, 16:34
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ahirjoy wrote: 2) In the xyplane, 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



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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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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



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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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30 May 2010, 13:23
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 xyplane, 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.
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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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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?



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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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31 May 2010, 04:18
Bunuel, thanks for the explanation.



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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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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..



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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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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 xs are negative and ys are positive, hence if point \((a,b)\) is in this quadrant, \(b\) (y coordinate of the point) is positive; In IV quadrant xs are positive and ys 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 viseversa). 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.
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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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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 xyplane, 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?
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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
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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 xyplane, 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? \(ab\neq{0}\) just means that neither \(a\) nor \(b\) equal zero, but we cannot say anything about their sings.
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Re: If ab <> 0 and points (a,b) and (b,a) are in the same [#permalink]
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22 Apr 2012, 19:10
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... 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.



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Re: If ab <> 0 and points (a,b) and (b,a) are in the same [#permalink]
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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
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