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Coordinate geometry

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by raju232007 » Tue Sep 30, 2008 1:11 pm
If ab is not equal to 0 and points (a,-b) & (b,-a) are in the same quadrant of the xy plane, is the point (-x,y) in the same quadrant?
1.xy>0
2.ax>0

The explanation for this problem has already been posted somewhere in this forum..but i still have my doubts on how to solve this one.ans is C..Kindly help...
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Source: — Data Sufficiency |
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by kris610 » Tue Sep 30, 2008 4:08 pm
I believe it should be B.

Given:

neither a nor b is 0.

(a,-b) and (b,-a) both lie in the same quadrant; Try giving a few examples with the same numbers but reversing the signs and you will notice that they should lie in the 2nd or the 4th quadrant i.e. a and b have opposite signs.

Now, your job is to figure out if (-x,y) lies in the same quadrant as these two points. How do you figure that? If you can tell that -x and y have the signs corresponding to a and b respectively.

A) tells you that x and y have the same sign, indicating -x and y have opposite signs,so (-x,y) lies either in the 2nd or the 4th quadrant. But this is not sufficient.

B) tells you that a and x have the same sign. This indicates a and -x are of opposite signs, which should be sufficient to say that (-x,y) does not lie in the same quadrant that contains (a,-b) and (b,-a). For example if a is positive, the points (a,-b) and (b,-a) will be in the 4th quadrant, but (-x,y) will be in the 2nd or the 3rd quadrant.

Am I missing something here?
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by 4meonly » Wed Oct 01, 2008 2:14 am
From the main statement we deduce that a and b are either both positive or both negative. Only in this case (-a;b) and (-b;a) can be in one quadrant – in II or in IV

(1)
xy>0
x and y can both negative and positive
(x positive)(y positive)>0 will be in the same quadrant
(x negative)(y negative)>0 will NOT be in the same quadrant
It is INSUFFICIENT

(2)
ax>0
a and x can both negative and positive
(a positive)(x positive)>0
(a negative)(x negative)>0
But we don know is a positive or negative!
It is INSUFFICIENT

(1) and (2)
This means that a, b, x and y are either ALL positive or all negative.
Here I substituted positive and negative meanings and found that taking (1) and (2) I can answer that (-a;b), (-b;a) and (-x;y) will always be in the same quadrant.
ANSWER - C
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by kris610 » Wed Oct 01, 2008 6:51 am
(2)
ax>0
a and x can both negative and positive
(a positive)(x positive)>0
(a negative)(x negative)>0
But we don know is a positive or negative!
It is INSUFFICIENT

If a and x have the same sign, wouldn't that mean a and -x have opposite signs. indicating (-x,y) is not in the same quadrant as (a,b)?
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by Thouraya » Fri May 06, 2011 4:22 am
Hi,

I am trying to solve this problem in that I am drawing a table showing the different scenarios. It's taking me a lot of time to figure out the different options. I figured out that a and b must both be negative or positive quickly; however, it is taking me time to figure out whether the (-x,y) will be in the same quadrant or not. Can an expert please give me a quick approach to tackle this in 2 mins or less?

Thank you!
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by Thouraya » Thu May 12, 2011 12:24 pm
Would greatly appreciate an Expert's help..Thanks!
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by djiddish98 » Thu May 12, 2011 1:33 pm
kris610 wrote:
B) tells you that a and x have the same sign. This indicates a and -x are of opposite signs, which should be sufficient to say that (-x,y) does not lie in the same quadrant that contains (a,-b) and (b,-a). For example if a is positive, the points (a,-b) and (b,-a) will be in the 4th quadrant, but (-x,y) will be in the 2nd or the 3rd quadrant.

Am I missing something here?
I think this is a good explanation (I got the question wrong) - I'm surprised it's C.
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by GMATGuruNY » Thu May 12, 2011 5:47 pm
raju232007 wrote:If ab is not equal to 0 and points (-a,b) & (-b,a) are in the same quadrant of the xy plane, is the point (-x,y) in the same quadrant?

1.xy>0
2.ax>0

The explanation for this problem has already been posted somewhere in this forum..but i still have my doubts on how to solve this one.ans is C..Kindly help...
This question is from GMATPrep. I've amended the information above to reflect that given in the original question.

Only two cases satisfy the constraint that (-a,b) and (-b,a) are in the same quadrant.

Case 1: Both a and b are positive
Let a=2, b=3.
Then (-a,b) = (-2,3) and (-b,a) = (-3,2).
Both points are in quadrant II.

Case 2: Both a and b are negative
Let a=-2, b=-3.
Then (-a,b) = (2,-3) and (-b,a) = (3,-2).
Both points are in quadrant IV.

Thus, for (-a,b) and (-b,a) to be in the same quadrant, a and b must have the same sign.
Implication:
For (-x,y) to be in the same quadrant as (-a,b) and (-b,a), x and y must have the SAME SIGN as a and b.

Question rephrased: Do x and y have the same sign as a and b?

Statement 1: xy > 0.
Here, x and y have the same sign.
No way to determine whether this sign is the same as that of a and b.
INSUFFICIENT.

Statement 2: ax>0.
Here, a and x have the same sign.
No information about y.
INSUFFICIENT.

Statements 1 and 2 combined:
Since x and y have the same sign, and a and x have the same sign, x, y, and a -- and thus b -- all have the same sign.
SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Tue Jun 25, 2013 7:22 am, edited 2 times in total.
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by djiddish98 » Thu May 12, 2011 6:24 pm
GMATGuruNY wrote:
Question rephrased: Are x and y the same sign, and is that sign different from that of a and b?


Statement 2: ax>0.
Thus, a and x are the same sign.
No information about y.
Insufficient.
If we know that x and a are the same sign, doesn't that prove that the point (-x,y) is NOT in the same quadrant as (a,-b)? Why do we need information about Y?
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by GMATGuruNY » Thu May 12, 2011 6:57 pm
djiddish98 wrote:
GMATGuruNY wrote:
Statement 2: ax>0.
Thus, a and x are the same sign.
No information about y.
Insufficient.
If we know that x and a are the same sign, doesn't that prove that the point (-x,y) is NOT in the same quadrant as (a,-b)? Why do we need information about Y?
I think that the confusion stems from typos in the question as posted.

I've amended my post above to reflect the information given in the original question, which is from GMATPrep. The correct answer to the GMATPrep question is C.

The correct answer to the question posted by raju232007 is B. If we know that a and x have the same sign, then we know that (-x,y) cannot be in the same quadrant as (a,-b) and (b,-a).
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by sahilchaudhary » Sun Nov 17, 2013 7:25 am
The difference in the question is:

"the same quadrant" as posted by raju232007 and "this same quadrant" as given in GMAT Prep.

Hope that helps!
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by Mathsbuddy » Sun Nov 17, 2013 12:57 pm
1.xy>0

This means that x and y are both positive (> 0)
Therefore (-x,y) is always in the 2nd quadrant.

2.ax>0

As x > 0, then a > 0 too (because positive * negative would otherwise be negative)

3. (a,-b) & (b,-a) are in the same quadrant

As a is positive, -a is negative and by matching coordinates, b is positive too as corresponding polarity must match in the same quadrant.

Therefore (a, -b) is in the 4th quadrant.

Therefore, (-x,y) is not in the same quadrant as (a, -b).
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by Mo2men » Sat Sep 14, 2019 7:27 pm
GMATGuruNY wrote:
raju232007 wrote:If ab is not equal to 0 and points (-a,b) & (-b,a) are in the same quadrant of the xy plane, is the point (-x,y) in the same quadrant?

1.xy>0
2.ax>0

The explanation for this problem has already been posted somewhere in this forum..but i still have my doubts on how to solve this one.ans is C..Kindly help...
This question is from GMATPrep. I've amended the information above to reflect that given in the original question.

Only two cases satisfy the constraint that (-a,b) and (-b,a) are in the same quadrant.

Case 1: Both a and b are positive
Let a=2, b=3.
Then (-a,b) = (-2,3) and (-b,a) = (-3,2).
Both points are in quadrant II.

Case 2: Both a and b are negative
Let a=-2, b=-3.
Then (-a,b) = (2,-3) and (-b,a) = (3,-2).
Both points are in quadrant IV.

Thus, for (-a,b) and (-b,a) to be in the same quadrant, a and b must have the same sign.
Implication:
For (-x,y) to be in the same quadrant as (-a,b) and (-b,a), x and y must have the SAME SIGN as a and b.

Question rephrased: Do x and y have the same sign as a and b?

Statement 1: xy > 0.
Here, x and y have the same sign.
No way to determine whether this sign is the same as that of a and b.
INSUFFICIENT.

Statement 2: ax>0.
Here, a and x have the same sign.
No information about y.
INSUFFICIENT.

Statements 1 and 2 combined:
Since x and y have the same sign, and a and x have the same sign, x, y, and a -- and thus b -- all have the same sign.
SUFFICIENT.

The correct answer is C.
Dear GMATGuru,

If the question asks the following:
is the point (x,y) in the same quadrant? (P.S.: I deleted the sign before x)

Does this make statement A sufficient.

Here, (x,y) will be either in quadrant 1 or 4 which does not match any quadrant of II or IV.

Am I correct?
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by GMATGuruNY » Thu Sep 19, 2019 9:11 am
Mo2men wrote:Dear GMATGuru,

If the question asks the following:
is the point (x,y) in the same quadrant? (P.S.: I deleted the sign before x)

Does this make statement A sufficient.

Here, (x,y) will be either in quadrant 1 or 4 which does not match any quadrant of II or IV.

Am I correct?
This line of reasoning is correct, but the red portion has a typo and should read "quadrant 1 or 3."
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