BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

quadrant problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members
Location: Milpitas, CA
Thanked: 447 times

by Rahul@gurome » Tue Oct 12, 2010 8:29 am
(1) xy > 0 implies that either both x and y should be positive or both should be negative. So, this is NOT SUFFICIENT to determine whether (-x,y) is in the same quadrant.

(2) ax > 0 implies that either a and x should be positive or both should be negative. But there is no info on y. So, (2) is NOT SUFFICIENT.

Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign.

[spoiler]The correct answer is (C).[/spoiler]
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Sun Dec 06, 2009 8:50 am
Thanked: 1 times

by ksundar » Thu Oct 14, 2010 7:45 pm
But b can be either a positive number or a negative number. which leaves us with -a.b and (-b,a) can be in the first or the second quadrant. If x and y are positive, then (-x,y) will be in the 2nd quadrant. If x and y are negative, coordinates would be in the 4th quadrant. So to me, with both statements we can say for sure that the three coordinates are in the same quadrant.

Please let me know if I am missing something.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 268
Joined: Wed Mar 17, 2010 2:32 am
Thanked: 17 times

by this_time_i_will » Sat Oct 16, 2010 1:57 am
if b is negative then first point would lie in IIIrd quadrant and second point would lie in Ist quadrant (ofcourse assuming that a is positive). This would not satisfy stmt. I
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Sun Feb 07, 2010 1:51 pm

by sandysai » Tue Oct 19, 2010 10:47 pm
Hi Rahul

if ab does not equal 0, and (-a.b) and (-b,a) are in the same quadrant, is (-x,y) in this quadrant?

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


Your earlier response:

"Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign"

I have QQ the above statement doesnt give any infernece abour B . To determin ( - x and y) lie in same co-ordinate, wht is there no dependency on "b" . How can we conclude with out considering b variable .?

Please throw some light on this one. Thanks!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members
Location: Milpitas, CA
Thanked: 447 times

by Rahul@gurome » Wed Oct 20, 2010 4:00 am
sandysai wrote:Hi Rahul

if ab does not equal 0, and (-a.b) and (-b,a) are in the same quadrant, is (-x,y) in this quadrant?

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


Your earlier response:

"Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign"

I have QQ the above statement doesnt give any infernece abour B . To determin ( - x and y) lie in same co-ordinate, wht is there no dependency on "b" . How can we conclude with out considering b variable .?

Please throw some light on this one. Thanks!!
Let's start from the beginning again! :)

Given: ab does not equal zero, and (-a,b) and (-b,a) are on the same quadrant. These implies,
(i) Neither a nor b is equal to zero (As ab does not equal to zero).
(ii) As (-a,b) and (-b,a) are on the same quadrant. -a and -b should be of same sign. Thus, a and b are of same sign.

These information are available from the question itself.

Statement 1: xy > 0. This implies, x and y are of same sign. Nothing is said about their relation with a or b. So, this is NOT SUFFICIENT to determine whether (-x,y) is in the same quadrant.

Statement 2: ax > 0. This implies, a and x are of same sign. But nothing is mentioned about y. So, this is NOT SUFFICIENT to determine whether (-x,y) is in the same quadrant.

Now if we take both the statements together, we have the following information,
(i) a and b are of same sign. (From the question itself)
(ii) x and y are of same sign. (From Statement 1)
(iii) a and x are of same sign. (From Statement 2)

Combining these information, we get that a, b, x and y are of same sign. Therefore (-a,b), (-b,a) and (-x,y) are in the same quadrant. So, the statements together are sufficient.

The correct answer is C.


Hope this clears the confusions.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 86
Joined: Mon Sep 13, 2010 2:36 pmFollowed by: 2 members
Thanked: 29 times
GMAT Score:710

by thebigkats » Wed Dec 22, 2010 2:23 pm
HI:
This is the thought process I followed to reach my conclusion:

1. (-a,b) and (-b, a) are in same qudrant as well as ab >0. taking a=2 and b=3 and placing different signs (4 combinations), I got to conclusion that either both are positive or both are negative (meaning that the point -a,b / -b,a is either in quadrant 2 or 4 (repalcing above no's ==> (-2, 3) /(-3, 2) _or_ (-(-2), -3) / (-(-3), -2)

2. STATEMENT #1 - xy >0
means that both are positive or negative (non-zero) - lets take (5,6) and (-5, -6). However this doesn't tell me much becasue (-x,y) = (-5, 6) or (5, -6) may be in opposite quadrant than where a and b are depending on their sign

3. STATEMENT #2 - ax >0
means that both a and x are same sign. given that a and b are also same sign - this means that -x,y may or may not fall in the same quardrant depending on y's sign which we don;t know from this statement alone

4. STATEMENT #1 and #2
means that y is also same sign as a, so all are of same sign and hence -a, b is in same quardrant as -b, a whcih is in same quardrant as -x,y
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Sat Oct 16, 2010 8:15 am
Thanked: 9 times

by Zerks87 » Thu Dec 30, 2010 12:25 pm
Rahul@gurome wrote:(1) xy > 0 implies that either both x and y should be positive or both should be negative. So, this is NOT SUFFICIENT to determine whether (-x,y) is in the same quadrant.

(2) ax > 0 implies that either a and x should be positive or both should be negative. But there is no info on y. So, (2) is NOT SUFFICIENT.

Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign.

[spoiler]The correct answer is (C).[/spoiler]
I liked Rahul's explanation but I also tried it a little differently.

Know: (-a, b) and (-b,a) are in the same quadrant

Want: is xy in this quadrant?

Visually setting up a coordinate plane here was helpful as I thought through this.

(1) xy > 0 - this means that x and y either have to be both positive or negative. If we assume that both (-a,b) and (-b,a) are in the upper right quadrant of the coordinate plane (however they could in any one), then those two coordinates are in a place where x>0 and y>0. So if x and y are both positive numbers then xy would be in this quadrant, but if x and y are both negative they would not be, since there are two possibilities (1) is INSUFF,.

(2) ax>0 - thing as statement (1), and we are not given any info about y. Clearly INSUFF

(1) + (2) - Since both -a and a are in the same quadrant (from stem), when you multiply it by either -x or x in accordance with statement (2) it will be in the same quadrant. since ax>0, they have the same signs, since xy>0 that means that they have the same signs, this by extention means that ay>0 and since a and -a are in the same quadrant this means that y or -y will work. Therefore both combinations of x and y should work too, SUFF.

The correct answer is C

Rahul could you comment on my logic here if it is possible to follow it?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 86
Joined: Mon Sep 13, 2010 2:36 pmFollowed by: 2 members
Thanked: 29 times
GMAT Score:710

by thebigkats » Thu Dec 30, 2010 12:41 pm
Hi Jerks87:

Re your post "Want: is xy in this quadrant? "

Isn't actual want "Want: is -x,y in this quadrant? "

Also given that ab > 0, a,b would never be in upper right quadrant and hence testing x,y against that location is incorrect - do you agree?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 90
Joined: Thu Nov 05, 2009 9:14 amFollowed by: 3 members
Thanked: 5 times

by immaculatesahai » Mon Dec 19, 2011 11:45 pm
C winner here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 382
Joined: Thu Mar 31, 2011 5:47 pm
Thanked: 15 times

by ArunangsuSahu » Wed Dec 28, 2011 12:13 am
According to the problem statement:
and b must be of same sign(as the points have to be in the same quadrant.(Try with actual nos)

(-x,y)

Statement 1:
xy >0 implies x and y are of same signs but no clear info about the quadrants. It can Quadrant 2 or Quadrant 4(test with values. So INSUFFICIENT

Statement 2:
ax > 0 implies and x are of same signs but no info about y. So INSUFFICIENT

Combining (1) and (2)
a,x, y have same signs. So SUFFICIENT
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Tue Nov 08, 2011 10:03 pm
Thanked: 2 times

by jayoptimist » Thu Jan 19, 2012 6:32 am
1. Given (-a,b) and (-b,a) are in the same quadrant. This means "a" and "b" have the same signs.(+,-)

1) xy > 0
Means x and y have the same signs. Good. But this does not tell us if the values are in the same quadrant as (-a,b) and (-b,a). Insufficient.

So we need something that links x and y to a and b.Come,Stmt 2
2) ax > 0
Means "a" and "x" have the same signs. The link we are looking for is found, but the statement in itself is insufficient.

Statements 1) + 2) says, a,x and y have the same signs.
Hence C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 626
Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members
Location: Ahmedabad
Thanked: 31 times

by ronnie1985 » Fri Mar 30, 2012 9:26 am
Rahul@gurome wrote:(1) xy > 0 implies that either both x and y should be positive or both should be negative. So, this is NOT SUFFICIENT to determine whether (-x,y) is in the same quadrant.

(2) ax > 0 implies that either a and x should be positive or both should be negative. But there is no info on y. So, (2) is NOT SUFFICIENT.

Combining (1) and (2), we get to know that x, y and a are all positive or all negative that x, y and a have the same sign.

[spoiler]The correct answer is (C).[/spoiler]
Yes but, knowing that a and x are of same sign guarantees that they are in the same quadrant, only which quadrant is not clear. If thought from this perspective (B) should be the answer.

Sorry i just ignored y.
Follow your passion, Success as perceived by others shall follow you
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 626
Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members
Location: Ahmedabad
Thanked: 31 times

by ronnie1985 » Fri Mar 30, 2012 9:29 am
S1 x and y are of same sign. Not Sufficient
S2 a and x are of same sign, y sign not clear
Comb: a,x and y are of same sign. Sufficient.
(C)
Follow your passion, Success as perceived by others shall follow you
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 308
Joined: Thu Mar 29, 2012 12:51 amFollowed by: 3 members
Thanked: 16 times

by Lifetron » Sat Jul 21, 2012 6:41 am
C ! :D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply