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# If ab is not equal to 0 and points (-a,b) and (-b,a) are in

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VP
Joined: 21 Jul 2006
Posts: 1361
If ab is not equal to 0 and points (-a,b) and (-b,a) are in  [#permalink]

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12 Apr 2008, 22:25
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If ab is not equal to 0 and points (-a,b) and (-b,a) are in the same quandrant of the xy-plane, is point (-x,y) in this same quadrant?

(1) xy > 0

(2) ax > 0

Can someone please explain to me in detail how to approach this problem? I just didn't know what to do here.
thanks

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SVP
Joined: 04 May 2006
Posts: 1605
Schools: CBS, Kellogg

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13 Apr 2008, 00:27
2
tarek99 wrote:
If ab is not equal to 0 and points (-a,b) and (-b,a) are in the same quandrant of the xy-plane, is point (-x,y) in this same quadrant?

(1) xy > 0

(2) ax > 0

For a=1, b=10

(-a,b) = (-1,10) belongs to II quandrant.
(-b,a) = (-10,1) belongs to II quandrant.

So (-a,b) and (-b,a) are in the same quandrant

For a= 1, b=-10

(-a,b) = (-1,-10) belongs to III quandrant.
(-b,a) = (10,1) belongs to I quandrant.
So (-a,b) and (-b,a) are not in the same quandrant

For a=-1, b=10
(-a,b) = (1,10) belongs to I quandrant.
(-b,a) = (-10,-1) belongs to III quandrant.
So (-a,b) and (-b,a) are not in the same quandrant

For a=-1, b=-10
(-a,b) = (1,-10) belongs to IV quandrant.
(-b,a) = (10,-1) belongs to IV quandrant.
So (-a,b) and (-b,a) belongs to the same quandrant

We conclude that (-a,b) and (-b,a) in the same quandirant only when a and b have the same sign.

From 1, x and y have the same sign, but no connection with a and b: Not sufficient

From 2, x and a have the same sign, again it has no connection with y: Not sufficient

1 and 2 combined: x, y and a have same sign, : Sufficient to concluion (-x,y)is in the same quandran.
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CEO
Joined: 17 May 2007
Posts: 2808

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14 Apr 2008, 21:35
Any other (preferably simpler) explanations for this ? Its a great question and kudos +1 to both poster and sondenso.
VP
Joined: 21 Jul 2006
Posts: 1361

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15 Apr 2008, 01:42
bsd_lover wrote:
Any other (preferably simpler) explanations for this ? Its a great question and kudos +1 to both poster and sondenso.

yeah, i'm also waiting for a simpler explanation. It's a great explanation already, but for the gmat, i prefer it to be simpler since we will not have the luxury of time on our side when taking the gmat. anyone?
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Joined: 09 Sep 2013
Posts: 11029
Re: If ab is not equal to 0 and points (-a,b) and (-b,a) are in  [#permalink]

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20 Jul 2017, 14:04
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Re: If ab is not equal to 0 and points (-a,b) and (-b,a) are in   [#permalink] 20 Jul 2017, 14:04
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