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# If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is

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If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  15 May 2010, 04:37
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 May 2013, 07:41, edited 2 times in total.
Added the OA
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Re: gmatprep ps [#permalink]  15 May 2010, 06:31
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If ab different from 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?

The fact that points (-a,b) and (-b,a) are in the same quadrant means that a and b have the same sign. These points can be either in II quadrant, in case a and b are both positive, as (-a,b)=(-,+)=(-b,a) OR in IV quadrant, in case they are both negative, as (-a,b)=(+,-)=(-b,a) ("=" sign means here "in the same quadrant").

Now the point (-x,y) will be in the same quadrant if x has the same sign as a (or which is the same with b) AND y has the same sign as a (or which is the same with b). Or in other words if all four: a, b, x, and y have the same sign.

Note that, only knowing that x and y have the same sign won't be sufficient (meaning that x and y must have the same sign but their sign must also match with the sign of a and b).

(1) xy>0 --> x and y have the same sign. Not sufficient.
(2) ax>0 --> a and x have the same sign. But we know nothing about y, hence not sufficient.

(1)+(2) x and y have the same sign AND a and x have the same sign, hence all four a, b, x, and y have the same sign. Thus point (-x,y) is in the same quadrant as points (-a,b) and (-b,a). Sufficient.

Answer: C.

For more in this topic check coordinate geometry chapter of math book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: Quadrants - Gmatprep [#permalink]  04 Jan 2012, 11:41
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Hi, there! I'm happy to help with this.

First, a quick review of quadrants: what defines the quadrants are the +/- signs of x and y

1) In Quadrant I, x > 0 and y > 0
2) In Quadrant II, x < 0 and y > 0
3) In Quadrant III, x < 0 and y < 0
4) In Quadrant VI, x > 0 and y < 0

If (-a, b) and (-b, a) are in the same quadrant, that means that the x-coordinates have the same sign, and also the y-coordinates have the same sign. Look at the y-coordinates --- if the two points are in the same quadrant, a & b have the same sign. They either could both be positive (in which case, the points would be in Quadrant II) or they could both be negative (in which case, the points would be in Quadrant IV).

Now, the question is: (-x, y) in the same quadrant as these two points?

(1) Statement 1: xy > 0

This tells us that x and y have the same sign --- both positive or both negative. Now, we know a & b have the same sign, and x & y have the same sign, but there's two possibilities for each, so we don't know whether a & b & x & y all have the same sign. This is insufficient.

(2) Statement 2: ax > 0

This, by itself, tells us that a and x have the same sign -- with this alone, we know that a & b & x all have the same sign, but we have zeor information about y. This too is insufficient.

Combined (1) & (2)
Prompt tells us a & b have the same sign. Statement #1 tells us x & y have the same sign. Statement #2 tells us x & a have the same sign. Put it all together --> we now know that x & y & a & b all have the same sign. Therefore, (-x, y) will have the same sign x- & y-coordinates as (-a, b) & (-b, a), and therefore all will be in the same quadrant. Combined statements are sufficient.

Answer = C

Here's another coordinate plane practice question just for practice.

http://gmat.magoosh.com/questions/1028

Does all that make sense? Please let me know if you have any additional questions.

Mike
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Re: Quadrants - Gmatprep [#permalink]  04 Jan 2012, 12:44
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Lets rephrase the stem first. For (-a,b) and (-b, a) to lie in same quadrant, both are either positive or negative.

1. xy>0, which means both are either positive or negative. Say a and b are positive, so they lie in IV. But xy could be ++ or --, causing it to lie in II or IV. Insufficient.

2. ax>0. which means positive or negative. What about y? No data on y causes this statement to be insufficient.

Together, means that a, x and y have same signs, therefore same quadrants. Sufficient - C.
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  15 Feb 2012, 15:51
Thanks everyone. But I am still getting confused between x, y a and b. Are we saying x and y as cordinates and a and b as points i.e. x(-a,b) and y(-b,a)?
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  15 Feb 2012, 16:05
Expert's post
enigma123 wrote:
Thanks everyone. But I am still getting confused between x, y a and b. Are we saying x and y as cordinates and a and b as points i.e. x(-a,b) and y(-b,a)?

We have 3 points with coordinates (-a,b), (-b,a) and (-x, y).

Also, check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it's clear.
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  15 Feb 2012, 16:09
Yes Bunuel - got it now. Thanks.
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  31 Mar 2012, 09:30
x & y have same sign is not sufficient.........

we have to identify they are in quadrant II 0r IV aswell.

hence C
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  30 Sep 2013, 11:48
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jitendra wrote:
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

A table will help ..

a b -a,b -b,a
+ + 2nd 2nd
+ - 3rd 1st
- + 1st 3rd
- - 4th 4th

you gotta know following:
+,+ >> 1st
-,+ >> 2nd
-,- >> 3rd
+,- >> 4th

this tells us (-a, b) and (-b, a) are either in 2nd quadrant or in 4th quadrant ..

1.) xy>0 means both have same sign and -x,y could be in 2nd or 4th quadrant .. its possible that -x,y is in 4th quadrant and (-a, b) and (-b, a) in 2nd and vice-a-versa .. hence insufficient

2.) ax>0 .. no info about y ... not sufficient

1+2 >> a and x both +ve 2nd qadrant
both negative, 4th quatrant .. hence -x,y and the points given in question will be in same quadrant .. C answer
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  30 Sep 2013, 11:49
jitendra wrote:
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

A table will help ..

a b -a,b -b,a
+ + 2nd 2nd
+ - 3rd 1st
- + 1st 3rd
- - 4th 4th

you gotta know following:
+,+ >> 1st
-,+ >> 2nd
-,- >> 3rd
+,- >> 4th

this tells us (-a, b) and (-b, a) are either in 2nd quadrant or in 4th quadrant ..

1.) xy>0 means both have same sign and -x,y could be in 2nd or 4th quadrant .. its possible that -x,y is in 4th quadrant and (-a, b) and (-b, a) in 2nd and vice-a-versa .. hence insufficient

2.) ax>0 .. no info about y ... not sufficient

1+2 >> a and x both +ve 2nd qadrant
both negative, 4th quatrant .. hence -x,y and the points given in question will be in same quadrant .. C answer
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  13 Oct 2013, 20:00
(1)+(2) x and y have the same sign AND a and x have the same sign, hence all four a, b, x, and y have the same sign. Thus point (-x,y) is in the same quadrant as points (-a,b) and (-b,a). Sufficient.

Bunuel, you are saying that (1)+(2) tells us that ALL a, b, x, and y have the same sign
Here's my doubt:
statements (1)+(2) give us info ONLY about the signs of a, x, and y.
You are telling that if "a, x, and y all have the SAME sign then b also has the same sign as a, x, and y."
How could you a say that because b does not form part of any of the statements (1) or (2)
So, what I mean to say is that b can be +ve or -ve irrespective of what signs a, x, and y take.
Please clear my doubt Bunuel.
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  13 Oct 2013, 23:19
Expert's post
madn800 wrote:
(1)+(2) x and y have the same sign AND a and x have the same sign, hence all four a, b, x, and y have the same sign. Thus point (-x,y) is in the same quadrant as points (-a,b) and (-b,a). Sufficient.

Bunuel, you are saying that (1)+(2) tells us that ALL a, b, x, and y have the same sign
Here's my doubt:
statements (1)+(2) give us info ONLY about the signs of a, x, and y.
You are telling that if "a, x, and y all have the SAME sign then b also has the same sign as a, x, and y."
How could you a say that because b does not form part of any of the statements (1) or (2)
So, what I mean to say is that b can be +ve or -ve irrespective of what signs a, x, and y take.
Please clear my doubt Bunuel.

The fact that points (-a,b) and (-b,a) are in the same quadrant means that a and b have the same sign.
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Re: Quadrants - Gmatprep [#permalink]  15 Oct 2013, 21:02
mikemcgarry wrote:
Hi, there! I'm happy to help with this.

First, a quick review of quadrants: what defines the quadrants are the +/- signs of x and y

1) In Quadrant I, x > 0 and y > 0
2) In Quadrant II, x < 0 and y > 0
3) In Quadrant III, x < 0 and y < 0
4) In Quadrant VI, x > 0 and y < 0

If (-a, b) and (-b, a) are in the same quadrant, that means that the x-coordinates have the same sign, and also the y-coordinates have the same sign. Look at the y-coordinates --- if the two points are in the same quadrant, a & b have the same sign. They either could both be positive (in which case, the points would be in Quadrant II) or they could both be negative (in which case, the points would be in Quadrant IV).

Can someone please provide insights in the above colored part.
I'm not sure if I would be able to deduce it under timed conditions. I know, this can be proved by taking hypothetical coordinates and see the behavior. However, I would like to understand it conceptually.

Please help.

Regards,
imhimanshu
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Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is [#permalink]  19 Nov 2013, 14:41
ab≠0 and points (-a,b) and (-b,a) are in the same quadrant → tells me that a and b are both + or -

(1) xy>0 → tells me that x and y are both + or -. Not suffient

(2) ax>0 → tells me that a, b and x are all + or -. Not suffient

(1)+(2) enabled me to answer the question: C
Re: If ab≠0 and (-a, b) and (-b, a) are in the same quadrant, is   [#permalink] 19 Nov 2013, 14:41
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