Is xy < 0 ? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 21 Jan 2017, 23:36
GMAT Club Tests

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is xy < 0 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 997
Location: Singapore
Followers: 22

Kudos [?]: 747 [1] , given: 36

GMAT ToolKit User
Is xy < 0 ? [#permalink]

Show Tags

New post 04 Aug 2010, 14:17
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

55% (01:56) correct 45% (00:43) wrong based on 258 sessions

HideShow timer Statistics

Is xy < 0 ?

(1) 1/x < 1/y
(2) x > 0
[Reveal] Spoiler: OA

_________________

Please press kudos if you like my post.

Expert Post
1 KUDOS received
Math Expert
User avatar
S
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93382 [1] , given: 10557

Re: Need solution ! [#permalink]

Show Tags

New post 04 Aug 2010, 22:01
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
nusmavrik wrote:
Is xy < 0 ?
1. 1/x < 1/y
2. x > 0


Is xy < 0 ?

Notice that the question basically asks whether x and y have the opposite signs.

(1) \(\frac{1}{x}<\frac{1}{y}\) --> \(x\) and \(y\) can have the same sign (\(x=2\) and \(y=1\)) as well as opposite signs (\(x=-2\) and \(y=1\)). Not sufficient.

(2) \(x>0\) --> no info about \(y\). Not sufficient.

(1)+(2) As from (2) \(x>0\) then \(\frac{1}{x}<\frac{1}{y}\) to hold true, \(y\) must also be positive (left hand side, \(\frac{1}{x}\) is positive and right hand side, \(\frac{1}{y}\), to be greater than that, must also be positive). So \(x\) and \(y\) have the same sign, they are both positive: \(xy>0\). Therefore the answer to the question is NO. Sufficient.

Answer: C.

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 997
Location: Singapore
Followers: 22

Kudos [?]: 747 [0], given: 36

GMAT ToolKit User
Re: Need solution ! [#permalink]

Show Tags

New post 04 Aug 2010, 23:06
Thanks Bunuel ! This question was a hard trap. Thanks for the awesome explanation.
_________________

Please press kudos if you like my post.

Expert Post
Math Expert
User avatar
S
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93382 [0], given: 10557

Re: Is xy < 0 ? [#permalink]

Show Tags

New post 22 Feb 2014, 12:09
Intern
Intern
avatar
Joined: 02 Mar 2010
Posts: 19
Followers: 0

Kudos [?]: 15 [0], given: 16

GMAT ToolKit User Premium Member
Re: Is xy < 0 ? [#permalink]

Show Tags

New post 01 Mar 2014, 11:11
Hey Bunuel,
Can you please let me know where I'm going wrong in the following method:
Statement1:
1/x < 1/y
Subtract 1/y from both sides: we get (y-x)/xy <0.
Therefore, either xy<0 or (y-x)<0.
If xy<0 then the answer to our question is YES both are opposite signs.
If y-x<0 -> y<x, then both can have same sign or opposite signs (ie.., y<x<0 OR y<0<x OR 0<y<x)
Therefore, Statement1 is INSUFFICIENT.
Statement2: 0<x so x is Positive but no information about y, So statement 2 is INSUFFICIENT.
(1) and (2) together:
We still have y<0<x or 0<y<x
Therefore, Both statements together are INSUFFICIENT. So E.
Thanks for your help! :)
Expert Post
Math Expert
User avatar
S
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93382 [0], given: 10557

Re: Is xy < 0 ? [#permalink]

Show Tags

New post 02 Mar 2014, 03:55
prsnt11 wrote:
Hey Bunuel,
Can you please let me know where I'm going wrong in the following method:
Statement1:
1/x < 1/y
Subtract 1/y from both sides: we get (y-x)/xy <0.
Therefore, either xy<0 or (y-x)<0.
If xy<0 then the answer to our question is YES both are opposite signs.
If y-x<0 -> y<x, then both can have same sign or opposite signs (ie.., y<x<0 OR y<0<x OR 0<y<x)

Therefore, Statement1 is INSUFFICIENT.
Statement2: 0<x so x is Positive but no information about y, So statement 2 is INSUFFICIENT.
(1) and (2) together:
We still have y<0<x or 0<y<x
Therefore, Both statements together are INSUFFICIENT. So E.
Thanks for your help! :)


\(\frac{y-x}{xy} <0\) means that y-x and xy have the opposite sign: +- or -+.

When combined we know that x is positive. Now, if y were negative, then \(xy<0\), thus \(y-x\) must be positive, but in this case \(y-x=negative-positive=negative\), thus this case is not possible, y is NOT negative --> y is positive --> \(xy=positive\).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 02 Mar 2010
Posts: 19
Followers: 0

Kudos [?]: 15 [0], given: 16

GMAT ToolKit User Premium Member
Re: Is xy < 0 ? [#permalink]

Show Tags

New post 02 Mar 2014, 17:08
Thanks Bunuel for this great explanation!
Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 127
Followers: 10

Kudos [?]: 93 [0], given: 1

Re: Is xy < 0 ? [#permalink]

Show Tags

New post 02 Mar 2014, 22:42
nusmavrik wrote:
Is xy < 0 ?

(1) 1/x < 1/y
(2) x > 0


Statement I is insufficient:

x = 2, y = 1 (1/2 < 1/1) (xy > 0) (NO)
x = -1, y = 2 (1/-2 < 1/2) (xy <0) (YES)

Statement II is insufficient:
y can be negative or positive

Combining is sufficient:

(1/x) < (1/y)
If 1/x is positive then 1/y is also positive which means y is also positive. Hence xy is greater than zero
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 13493
Followers: 576

Kudos [?]: 163 [0], given: 0

Premium Member
Re: Is xy < 0 ? [#permalink]

Show Tags

New post 15 Jun 2015, 08:15
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
1 KUDOS received
Optimus Prep Instructor
User avatar
B
Joined: 06 Nov 2014
Posts: 1782
Followers: 51

Kudos [?]: 393 [1] , given: 21

Is xy < 0 ? [#permalink]

Show Tags

New post 16 Jun 2015, 08:09
1
This post received
KUDOS
Expert's post
Is xy < 0 ?
It's sometimes helpful to think of disproving rather than proving the statement. For xy to be negative, x and y have to be opposite signs.
(1) 1/x < 1/y For this statement consider x and y being both positive or both negative. For example, (1/4) <(1/2) or (-1/2) < (-1/4). Not sufficient.

(2) x > 0 We're given nothing about y so it could be positive as well. Not sufficient.

Multiply both sides of (1/x) < (1/y) by x to give (x/y) > 1 From statement 2 we know that x is positive. For x/y to be greater than one y also has to be positive. Sufficient (no)
C
_________________

Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring
GMAT On Demand Course $299
Free Online Trial Hour

BSchool Forum Moderator
User avatar
B
Joined: 12 Aug 2015
Posts: 1901
Followers: 49

Kudos [?]: 368 [0], given: 454

GMAT ToolKit User CAT Tests
Re: Is xy < 0 ? [#permalink]

Show Tags

New post 07 Mar 2016, 20:26
nusmavrik wrote:
Is xy < 0 ?

(1) 1/x < 1/y
(2) x > 0


statement 1=> not sufficient
statement 2 => not sufficient
combing them we get x/y>1
hence x/y>0 9as it is greater than 1 it must be greater than 0 )
so xy>0 (xy and x/y have the same sign)

thus C is sufficient
_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Mock Test -2 (Evensand Odds Basic Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023

Give me a hell yeah ...!!!!!

BSchool Forum Moderator
User avatar
B
Joined: 12 Aug 2015
Posts: 1901
Followers: 49

Kudos [?]: 368 [0], given: 454

GMAT ToolKit User CAT Tests
Re: Is xy < 0 ? [#permalink]

Show Tags

New post 13 Mar 2016, 05:38
Here to add to the explanation => X IS ALWAYS POSITIVE AND Y IS ALWAYS POSITIVE TOO => XY>0
the key to solving these question is to look out for a sufficient YES or a sufficient NO
_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Mock Test -2 (Evensand Odds Basic Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023

Give me a hell yeah ...!!!!!

Director
Director
avatar
B
Joined: 21 Jun 2014
Posts: 504
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Followers: 12

Kudos [?]: 167 [0], given: 92

Premium Member CAT Tests
Re: Is xy < 0 ? [#permalink]

Show Tags

New post 09 Apr 2016, 04:37
nusmavrik wrote:
Is xy < 0 ?

(1) 1/x < 1/y
(2) x > 0


are x and y of opposite sign??

stmt1- 1/x < 1/y
1/5 < 1/3 both positive
-1/3 < -1/5 both positive
-1/3 < 1/5 x negative y positive
insuff

stmt-2 x > 0, what about y??

both stmts:
if x is positive then 1/x < 1/y will hold true only when y is positive. hence x and y have same sign and xy>0.
suff
_________________

---------------------------------------------------------------
Target - 720-740
helpful post means press '+1' for Kudos!
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

Re: Is xy < 0 ?   [#permalink] 09 Apr 2016, 04:37
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Is xy < 0? Bunuel 3 14 Jan 2017, 08:00
2 Experts publish their posts in the topic Is xy < 0? AbdurRakib 2 11 Jun 2016, 09:17
5 Experts publish their posts in the topic If xy > 0, is (xy)^2<√xy ? Bunuel 3 29 Apr 2016, 02:53
Experts publish their posts in the topic If xy ≠ 0, is x/y < 0? janani28 2 06 Oct 2014, 08:35
9 Experts publish their posts in the topic Is xy < 0 ? carcass 8 08 May 2012, 02:25
Display posts from previous: Sort by

Is xy < 0 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.