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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?

xy >0 ax >0

stat 1 , where x and y can both be negative or positive. - not sufficient stat 2, where a and y can both be negative or positive, not sufficient

I'm guessing C. Please provide some explanation.

Thanks

a and b have the same sign: either both are positive or both are negative. 1: xy > 0 -> x and y have the same sign //not sufficient a(b) and x(y) can have different signs 2: ax > 0 -> a and x have the same sign -> a,x,b have the same sign, but don't know about y -> insufficient

1&2: a,b,x,y have the same sign -> (a,b) and (x,y) are in the same quadrant (sufficient) -> C

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?

xy > 0 ax > 0

I am not able to understand the problem, is it saying that a = 1, b =2 so (-1,2) (-2,1) lies in the same quadrant i'e quadrant I or that a = -1 , b =2 so (1,2)(2,1) lies in the same quadrant ie' quadrant II or that a = -1, b=-2 so (1,-2), (2,-1) lies in the same quadrant ie quadrant III.

does (-x,y) lie in either one of these quadrants. ?

if yes, (1) xy > 0, which means that they both are -ve or +ve. they could lie in quadr 1 or quadrant 11. sufficient

ax > 0, a and x are -ve, or +ve. - I don't get it . please help
_________________

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?

xy > 0 ax > 0

I am not able to understand the problem, is it saying that a = 1, b =2 so (-1,2) (-2,1) lies in the same quadrant i'e quadrant I or that a = -1 , b =2 so (1,2)(2,1) lies in the same quadrant ie' quadrant II or that a = -1, b=-2 so (1,-2), (2,-1) lies in the same quadrant ie quadrant III.

does (-x,y) lie in either one of these quadrants. ?

if yes, (1) xy > 0, which means that they both are -ve or +ve. they could lie in quadr 1 or quadrant 11. sufficient

ax > 0, a and x are -ve, or +ve. - I don't get it . please help

_________________ GMAT the final frontie!!!.
_________________

This question is referring to the chart on the quadrant plain: First draw the axes and label the x,y values for positive and negative.

I (a, b) II (a, -b) III (-a, -b) IV (-a, b)

The info in the question stem indicates -a,b and b,-a can both be in the fourth quadrant. So, looking at -x,y, can they be in the same quarter? According to (1), xy > 0. Therefore, x and y are either both negative or both positive. If x and y are both negative, could we find -x, y in the fourth quadrant? The answer is NO. If we had both x and y positive, could we find -x, y in the fourth quadrant? The answer is YES.

Moving to (2). For reasons similar to (1) and because a, an unrelated value is a part of the expression, this does not work either

Moving on to (1) and (2). Can they both work together? That's as far as I got. Can anyone else help?

First of all we need to put question in simple understadable terms. What does points (-a,b) and (-b, a) are in the same quadrant of the xy-plane implies? This simply means a and b have same signs. Either both of them are +ve or both of them are -ve. Also given ab not equal to 0. Question is asking is point (-x,y) in the same quadrant, which essentially means is X and Y have same signs as a or b?

Statement 1: xy > 0. This implies X and Y are both +ve or -ve. This is half the information. From question we know that a or b either +ve or -ve. But if a or b are +ve and x,y are -ve then they are not in same quadrant. Insufficient so A or D cannot be answer.

Statement 2: ax > 0. This implies a and x are both +ve or -ve. This is half the information. Because we know nothing about Y, in which quadrant it is. Insufficient so B cannot be answer.

By combining we know a, b, x, and y are all in same quadrant.

I have a question. (-a,b) and (-b,a) being in the same quadrant doesn't necessarily mean that a and b have the same sign because they could be in quadrant 2 or 4 where one of them is positive and the other is negative. would you please explain? i'm confused with this problem! thanks!

Points (-a,b) and (-b,a) are in the same quadrant mean -a and -b have the same sign (we can write ab>0) AND b and a have the same sign (which translates into ab>0 as well).

Point (-x,y) would be on the same quadrant if and only if -x had the same sign as -a and -b (i.e. ax>0 and bx>0) AND y had the same sign as b and a (i.e. by>0 and ay>0)

(1) tells us x and y have the same sign, but it gives no information about that sign relative to a and b signs ==> insufficient

(2) tells us -x has the same sign as -a and thus -b. But we don't know anything about the sign of y ==> insufficient

(1) and (2) tell us that -x has the same sign as -a and thus -b and that y has the same sign as x so that y has the same sign as a and b: (-x,y) IS in the same quadrant ==> sufficient

I have a question. (-a,b) and (-b,a) being in the same quadrant doesn't necessarily mean that a and b have the same sign because they could be in quadrant 2 or 4 where one of them is positive and the other is negative. would you please explain? i'm confused with this problem! thanks!

Your are right on the point. If in doubt take example is such kind of cases. Says take 4 case (1,1), (1,-1), (-1,1), (-1,-1) When (1,1) and (-1,-1) are taken then (-a,b) and (-b,a) fall in same quadrant. When (1,-1) and (-1,1) are taken then (-a,b) and (-b,a) do not fall in same quadrant.

This should make you 100% sure that your thinking is correct.

The fact (-a,b) and (-b,a) are in the same quadrant meens that a and b have the same sign, ie, they are both positive or both negative. So (-b,a) and (-a,b) can be in quarters 4 or 2.

1 says: x*y>0 wich meen that x and y have the same sign.

So (-x,y) can be in quarter 4 or 2.

We dont know if (-x,y) is in quarter 4 or 2,and the same for (-b,a) and (-a,b), so 1 is ins

2 says: a and x have the same sign--> ins because we dont know anyting about y.

fron 1 and 2 we know that a,b,x,y have the same sign, so (-x,y) must be in the same quarter as (-a,b) and (-b,a). -->Suffishent

if ab != 0 (unequal) and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant?

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

Looks so simple, but I found it very confusing. Will appreciate a clear explanataion.

For (-a,b) and (-b, a) to be in same quadrant, a and b have to have same signs meaning they are both either negative or positive. Therefore, ab > 0 Combining 1) and 2) we have three equations ab > 0 xy > 0 ax > 0

Now you will see if we pick a negative value for a [you can alterantivelyp pick b,x or y], we will get negative values for b,x and y if we pick +ve value for a, we get +ve values for x,y and b

Find the slope of the line formed by (-a,b) and (-b,a) Slope = (a-b)/(-b+a) = 1 Positive slope means, they are in either 1st or 3rd quandrant that means, either x and y are both positive or negative

a. xy greater than zero. Question asks for (-x,y) to be in I or III and the answer is No - SUFFICIENT

If ab is not 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant ?

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

IMO C

From what is given, it is clear a and b have the same sign (ie either both are positive or both are negative)

(i) Informs that x and y have the same sign But it is not clear their relationship with a or b and hence can't say which quadrant do they belong.

(ii) This informs that a and x are of the same sign also (ie either both of them are negative or both of them are positive) ii alone does not inform the relationship with y

However, combining them, gives a, b, x and y are all of the same sign. Thus (-x,y) will be in the same quadrant as (-a, b) and (-b, a)

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