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If ab not equals to 0, and points (-a,b) and(-b,a) are in

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Manager
Status: Stanford GSB
Joined: 02 Jun 2008
Posts: 86
If ab not equals to 0, and points (-a,b) and(-b,a) are in  [#permalink]

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11 Jan 2009, 23:49
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If ab not equals to 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

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Manager
Status: Stanford GSB
Joined: 02 Jun 2008
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Re: DS- Coordinate Geometry ( GMAT prep)  [#permalink]

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13 Jan 2009, 14:27
1
OA is C.
Intern
Joined: 20 Aug 2008
Posts: 20
Re: DS- Coordinate Geometry ( GMAT prep)  [#permalink]

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13 Jan 2009, 17:00
2
sandipchowdhury wrote:
OA is C.

Two points (x1, y1) and (x2, y2) will be in the same quadrant only if x1x2>0 AND y1y2>0

Given that (-a,b) and (-b,a) are in the same quad, we know that ab>0. Therefore a and b are of same sign.

For (-x,y) to be in the same quadrant, we need to show either (ax>0 AND by>0) OR (bx>0 AND ay>0).

1. xy > 0 . Insufficient
2. ax > 0. Insufficeint. we need by>0 as well.

1+2. ax>0 -- implies a and x are of same sign. Also xy > 0 -- implies x an y are of same sign. Given that a and b are of same sign. Therefore: a, b, x, y are all of same sign. Hence sufficeint.
Manager
Status: Stanford GSB
Joined: 02 Jun 2008
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Re: DS- Coordinate Geometry ( GMAT prep)  [#permalink]

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13 Jan 2009, 22:44
Superb explanation apshma
1 kudo to you.

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Re: If ab not equals to 0, and points (-a,b) and(-b,a) are in  [#permalink]

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09 Mar 2019, 11:00
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Re: If ab not equals to 0, and points (-a,b) and(-b,a) are in   [#permalink] 09 Mar 2019, 11:00
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