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Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
12 Mar 2010, 15:30

2

This post received KUDOS

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

Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
12 Mar 2010, 15:34

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

Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
30 May 2010, 12:23

1

This post received KUDOS

Expert's post

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.

Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
03 Jun 2010, 04:39

Expert's post

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).

Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
08 Mar 2012, 12:55

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?
_________________

Re: Coordinate Geometry Data Sufficiency Questions [#permalink]
08 Mar 2012, 13:00

Expert's post

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?

ab\neq{0} just means that neither a nor b equal zero, but we cannot say anything about their sings.
_________________

Re: If ab <> 0 and points (-a,b) and (-b,a) are in the same [#permalink]
22 Apr 2012, 18:57

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.

gmatclubot

Re: If ab <> 0 and points (-a,b) and (-b,a) are in the same
[#permalink]
22 Apr 2012, 18:57