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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.

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

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07 Dec 2011, 11:43

I took my first GmatPrep today after studying Quant for a month(Working on a 3month plan suggested by gmatclub experts). I haven't touched Verbal yet and my score was 660 (Q49V31) although i was a little disturbed about my Verbal score since i expected better, i was pretty surprised how getting 13 questions wrong in Quant got me to 49. But since GMAT is adaptive i guessed its possible. Anyways, i reworked the incorrect questions after the exam and cracked a few of them, however there are a few others that just stumped me completely even after giving them a 2nd shot.

1. If ab!=0 and point (-a,b) and (-b,a) are in the same quadrant ,does point (-x,y) lie in this quadrant? i) xy>0 ii) ax>0

There are a few others coming up..Please let me know if I made a rookie mistake by posting these here when it should be in some other forum category, I searched a lot couldn't really find any other suitable place. Thanks

Last edited by ijoshi on 07 Dec 2011, 18:28, edited 2 times in total.

1. If ab!=0 and point (-a,b) and (-b,a) are in the same quadrant ? i) xy>0 ii) ax>0

I think you've missed part of the question here - I think the question says:

If (-a, b) and (-b, a) are in the same quadrant, is the point (-x, y) in the same quadrant as (-a, b)? 1) xy > 0 2) ax > 0

If two points are in the same quadrant, then their x-coordinates have the same sign, and their y-coordinates have the same sign. So from the information that (-a, b) and (-b, a) are in the same quadrant, we learn that a and b have the same sign (either by looking at x-coordinates or at y-coordinates). So we know that a and b are either both positive or both negative, and that the point (-a, b) thus has one negative coordinate and one positive coordinate. The problem is we don't know which coordinate is positive, and which negative; it could be (+, -) or it could be (-, +).

From Statement 1, we learn that x and y have the same sign. Thus the point (-x, y) has coordinates of opposite signs. This point could be (+, -) or (-, +), so we don't know if it's in the same quadrant as (-a, b).

Statement 2 doesn't mention y at all, so cannot be sufficient, since we need to know about the sign of y.

Combining the two statements we know a and b have the same sign (from the stem), a and x have the same sign (from Statement 2) and x and y have the same sign (from Statement 1). So a, b, x and y all have the same sign. Thus the x-coordinates of (-a, b) and (-x, y) have the same sign, as do their y-coordinates, and the two points must be in the same quadrant. The answer is C.
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Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr [#permalink]

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18 Dec 2011, 16:48

(-a, b) and (-b, a) are in the same quadrant. Is the point (-x, y) in the same quadrant as point (-a, b)?

(1) xy > 0 (2) ax > 0

From the information that (-a, b) and (-b, a) are in the same quadrant, it can be determined that (-a, b) is in either quadrant II or quadrant IV. If (x, y) and (a, b) are in the same exact quadrant, they will have the same sign and (-x, y) will be in the same quadrant as (-a, b)'s.

(1) xy > 0

(x, y) is in quadrant I or quadrant III. (-x, y) is in quadrant II or quadrant IV. No further information is provided about (-a, b).

(2) ax > 0

Point x in (x, y) has the same sign as does point a in (a, b). Since a and b have the same sign, x, a and b have the same sign.

But the sign of point x could be different from, or the same as, the sign of point y. The condition that (x, y) and (a, b) have the same sign, and therefore that (-x, y) and (-a, b) are in the same quadrant, is possible but uncertain.

Combined analysis:

x has the same sign as y x has the same sign as a and b x, y, a and b all have the same sign.

This means (x, y) and (a, b) are in the same quadrant. (-x, y) and (-a, b) are in the same quadrant.

[xyab+xdj]

Last edited by Study1 on 31 Jan 2012, 16:26, edited 3 times in total.

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.

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

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04 Jan 2012, 13:44

1

This post received KUDOS

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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DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

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

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15 Feb 2012, 16:51

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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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).

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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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 points (-a, b) and (-b, a) are in the same quadr [#permalink]

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13 Oct 2013, 21:00

(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.

(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: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr [#permalink]

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15 Oct 2013, 22:02

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.

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

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31 Jul 2014, 01:45

Hello from the GMAT Club BumpBot!

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

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10 Sep 2014, 12:08

Bunuel wrote:

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.

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.

Hey Bunuel just asking a relevant doubt. Does ( -b,-a) or (-a,-b) lies in the same quadrant as (a,b) ?

Do you mean generally? If yes, then:

(a, b) and (-a, -b) will never be in the same quadrant.

(a, b) and (-b, -a) will be in the same quadrant if a is positive and b is negative, in this case (a, b) = (+, -) and (-b, -a) = (+, -) OR when a is negative and b is positive, in this case (a, b) = (-, +) and (-b, -a) = (-, +).
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Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr [#permalink]

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19 Sep 2015, 04:53

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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