GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 Feb 2020, 17:51

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Aug 2006
Posts: 63
Location: Mumbai
If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

Updated on: 31 Jul 2014, 01:52
12
1
83
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:29) correct 57% (02:22) wrong based on 758 sessions

### HideShow timer Statistics

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

Originally posted by jitendra on 15 May 2010, 04:37.
Last edited by Bunuel on 31 Jul 2014, 01:52, edited 3 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 61524
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

15 May 2010, 06:31
30
20
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.

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

Hope it helps.
_________________
##### General Discussion
Intern
Joined: 31 Oct 2011
Posts: 20
Location: United Arab Emirates
GMAT 1: 700 Q45 V40
GPA: 3.41
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

Updated on: 07 Dec 2011, 17:28
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

Originally posted by ijoshi on 07 Dec 2011, 10:43.
Last edited by ijoshi on 07 Dec 2011, 17:28, edited 2 times in total.
Intern
Joined: 14 Sep 2010
Posts: 11
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

Updated on: 31 Jan 2012, 15:26
1
(-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

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]

Originally posted by Study1 on 18 Dec 2011, 15:48.
Last edited by Study1 on 31 Jan 2012, 15:26, edited 3 times in total.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4475
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

04 Jan 2012, 11:41
11
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.

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
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager
Joined: 29 Jul 2011
Posts: 71
Location: United States
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

04 Jan 2012, 12:44
1
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.
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

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)?
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 61524
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

15 Feb 2012, 16:05
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.
_________________
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

15 Feb 2012, 16:09
Yes Bunuel - got it now. Thanks.
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Manager
Joined: 20 Jun 2012
Posts: 72
Location: United States
Concentration: Finance, Operations
GMAT 1: 710 Q51 V25
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

30 Sep 2013, 11:48
1
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
Manager
Joined: 07 May 2013
Posts: 86
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 61524
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

13 Oct 2013, 23:19
(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.

The fact that points $$(-a,b)$$ and $$(-b,a)$$ are in the same quadrant means that $$a$$ and $$b$$ have the same sign.
_________________
Manager
Joined: 07 Sep 2010
Posts: 245
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

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.

Regards,
imhimanshu
Intern
Joined: 14 Mar 2013
Posts: 41
Location: United States
GMAT Date: 12-03-2013
WE: General Management (Retail)
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

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
Manager
Joined: 09 Nov 2013
Posts: 61
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

10 Sep 2014, 11:08
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.

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

Hope it helps.

Hey Bunuel just asking a relevant doubt. Does ( -b,-a) or (-a,-b) lies in the same quadrant as (a,b) ?
Math Expert
Joined: 02 Sep 2009
Posts: 61524
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

10 Sep 2014, 11:39
Sidhrt wrote:
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.

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

Hope it helps.

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) = (-, +).
_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3265
Location: India
GPA: 3.12
Re: If ab ≠ 0 and points (–a, b) and (–b, a) are in the same quadrant ..  [#permalink]

### Show Tags

10 Jun 2017, 00:56
From the question stem, we can clearly tell that (–a, b) and (–b, a) are in the same quadrant
if both a,b are positive or negative.
We are asked to find if the point(-x,y) is also in the same quadrant

1. if xy > 0 , both x and y are postive, or both their values are negative are two options available.
When x and y are positive, if a and b are negative, they will not be in same quadrant.
But, if x and y are postive and a and b are also positive, these points will be in the same quadrant
Hence, insufficient.

2. ax > 0, both a and x are positive or both of them are negative.
When a and x are postive, b and y can be both negative or positive.
In one of the cases, we will have a YES, , for the point(-x,y) being in the same quadrant.
whereas in the other case, we will have a NO, for the point(-x,y) being in the same quadrant.
Hence insufficient.

But on combining the two, either a,b,x,y are all negative or all positive and clearly lie in the same quadrant
Sufficient(Option C)
_________________
You've got what it takes, but it will take everything you've got
Director
Joined: 29 Jun 2017
Posts: 967
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

27 Sep 2019, 08:09
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

we can infer that a and b are the same sign
pick numbers noun
a=b=1, the two points are at quater 2
x=1, y=1, it is in quater 1
x=-1, y=-1, the point is quater 2.
condition 1 is not enough

we can do this way. pick specific numbers for easy understanding.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10123
Location: Pune, India
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

03 Oct 2019, 03:15
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

ab≠0 means neither a nor b can be 0.

(-a, b) and (-b, a) are in the same quadrant of the xy-plane - In a quadrant, all x co-ordinates have the same sign and all y co-ordinates have the same sign e.g. all x coordinates are positive and all y coordinates are also positive in the first quadrant. Similarly, all x coordinates are negative and all y coordinates are positive in the second quadrant and so on...

So sign of -a and sign of -b should be the same. This means a and b must have the same signs. So either a and b are both positive such that (-a, b) is in second quadrant or both negative such that (-a, b) is in fourth quadrant.

Ques: is point (-x, y) in the same quadrant?

For (-x, y) to be in the same quadrant as (-a, b) and (-b, a), signs of x and y should be same and they should be the same as the sign of a and b.
If a and b are positive, (-x, y) should lie in the second quadrant so x and y should be positive too.
If a and b are negative, (-x, y) should lie in the fourth quadrant so x and y should be negative too.

(1) xy > 0

'x' and 'y' have the same sign but is the sign same as that of 'a' and 'b'? We don't know.

(2) ax > 0

'a' and 'x' have the same sign but is the sign of 'y' same too? We don't know.

Both together we know that 'x' and 'y' have the same sign and their sign is the same as the sign of 'a' too. Sufficient.

_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 09 Jun 2019
Posts: 90
GMAT 1: 570 Q42 V29
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr  [#permalink]

### Show Tags

25 Nov 2019, 05:35
Hi mikemcgarry,

One thing regarding this question has been bugging my mind, could you please help me with it?

For some reason, I cannot get the notion out of my head that the quadrants always have to be in the following formats:

However, if we take the signs of both "a" and "b" to be negative then couldn't it look different?
Lets say: a = -2 and b = -3 then we know that these point falls on the 3rd quadrant but while putting the values in (-a, b) and (-b, a) they would come to be as (2, -3) and (3, -2) which are the standard form of the 4th quadrant (x, -y) isn't it?
Now I know while plotting the values they would fall on the 3rd quadrant but its the confidence that I am lacking when tackling a similar question.

Thank You,
Dablu
Re: If ab≠0 and points (-a, b) and (-b, a) are in the same quadr   [#permalink] 25 Nov 2019, 05:35

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by