GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Oct 2018, 07:25

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

Is x + y > 0 ?

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

Hide Tags

Manager
Manager
User avatar
S
Joined: 13 Oct 2013
Posts: 131
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User Premium Member CAT Tests
Is x + y > 0 ?  [#permalink]

Show Tags

New post Updated on: 15 Jul 2014, 14:14
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:20) correct 38% (01:18) wrong based on 214 sessions

HideShow timer Statistics

Is x + y > 0 ?

(1) x - y > 0
(2) x^2 - y^2 > 0

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)


Originally posted by sunita123 on 15 Jul 2014, 13:58.
Last edited by Bunuel on 15 Jul 2014, 14:14, edited 2 times in total.
Edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49912
Is x + y > 0 ?  [#permalink]

Show Tags

New post 15 Jul 2014, 14:18
Is x + y > 0 ?

(1) x - y > 0 --> x > y. One number is greater than another. From this we cannot say whether their sum is positive. Not sufficient.

(2) x^2 - y^2 > 0 --> x^2 > y^2 --> |x| > |y|. One number is further from 0 than another. From this we cannot say whether their sum is positive. Not sufficient.

(1)+(1) From (2) (x - y)(x + y) > 0 (x + y and x - y have the same sign) and from (1) x - y > 0, thus x + y > 0. Sufficient.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1883
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 22 Apr 2016, 00:17
1
achintsodhi wrote:
Is x + y > 0?

(1) x – y > 0

(2) \(x^2 – y^ 2 > 0\)


Statement 1: x – y > 0
This means x > y
Case 1: x = 2, y = 1
Here x + y > 0
Case 2: x = -10, y = -11
Here x + y < 0
Insufficient

Statement 2: \(x^2 – y^ 2 > 0\)
Or \(x^2 > y^ 2\)
From this too, we cannot say anything about x + y
Case 1: x = 4, y = 1
x + y > 0
Case 2: x = -4, y = 1
x + y < 0
Insufficient

Statement 1 and 2 Combined:
From statement 1, x - y > 0
From statement 2, \(x^2 – y^ 2 > 0\) or (x+y)(x-y) >0
Since we already know that (x-y) > 0 from statement 1,
Therefore x + y > 0
Sufficient

Correct Option: C
Manager
Manager
avatar
Joined: 28 Jun 2016
Posts: 207
Location: Canada
Concentration: Operations, Entrepreneurship
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 07 Nov 2016, 17:03
1
felippemed wrote:
Is \(x + y >0\)?

(I) \(x - y > 0\)
(II) \(x^2 - y^2 > 0\)



Statement 1:

x>y

If both x and y are positive then YES

If both x and y are negative then NO

Insufficient

Statement 2:

(x+y)(x-y)>0

If x-y>0, then YES

If x-y<0, then NO

Insufficient

Statement 1&2:

x-y>0,

then x+y>0

Sufficient

C


Sent from my iPhone using GMAT Club Forum mobile app
Manager
Manager
User avatar
B
Joined: 23 Jun 2009
Posts: 184
Location: Brazil
GMAT 1: 470 Q30 V20
GMAT 2: 620 Q42 V33
GMAT ToolKit User Premium Member
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 07 Nov 2016, 18:49
Posted from my mobile device

Maybe a better approach is theoretically.

Posted from my mobile device
Manager
Manager
User avatar
B
Joined: 23 Jun 2009
Posts: 184
Location: Brazil
GMAT 1: 470 Q30 V20
GMAT 2: 620 Q42 V33
GMAT ToolKit User Premium Member
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 07 Nov 2016, 18:52
acegmat123 wrote:
felippemed wrote:
Is \(x + y >0\)?

(I) \(x - y > 0\)
(II) \(x^2 - y^2 > 0\)



Statement 1:

x>y

If both x and y are positive then YES

If both x and y are negative then NO

Insufficient

Statement 2:

(x+y)(x-y)>0

If x-y>0, then YES

If x-y<0, then NO

Insufficient

Statement 1&2:

x-y>0,

then x+y>0

Sufficient

C


Sent from my iPhone using GMAT Club Forum mobile app


I am not sure your approach is correct.

You could have a gigantic positive x e a tiny negative y and still hold the conditions true.
Manager
Manager
avatar
Joined: 28 Jun 2016
Posts: 207
Location: Canada
Concentration: Operations, Entrepreneurship
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 07 Nov 2016, 19:08
felippemed wrote:
acegmat123 wrote:
felippemed wrote:
Is \(x + y >0\)?

(I) \(x - y > 0\)
(II) \(x^2 - y^2 > 0\)



Statement 1:

x>y

If both x and y are positive then YES

If both x and y are negative then NO

Insufficient

Statement 2:

(x+y)(x-y)>0

If x-y>0, then YES

If x-y<0, then NO

Insufficient

Statement 1&2:

x-y>0,

then x+y>0

Sufficient

C


Sent from my iPhone using GMAT Club Forum mobile app


I am not sure your approach is correct.

You could have a gigantic positive x e a tiny negative y and still hold the conditions true.



Is it in Statement 1 or 2 or 1&2 taken together?
Intern
Intern
avatar
B
Joined: 01 Aug 2016
Posts: 27
Schools: ISB '18
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 07 Nov 2016, 22:19
1)x-y>0 is insufficient as it will show x>y but if x and y are negative then x+y can't be greater than 0. (Insufficient)
2)(x+y)(x-y)>0 is insufficient as we can't say whether x+y>0 or not

Combining we can say x+y>0.. So Answer is C
Manager
Manager
User avatar
B
Joined: 23 Jun 2009
Posts: 184
Location: Brazil
GMAT 1: 470 Q30 V20
GMAT 2: 620 Q42 V33
GMAT ToolKit User Premium Member
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 08 Nov 2016, 04:45
Quote:
Is it in Statement 1 or 2 or 1&2 taken together?


The answer is C, but the approach is a bit more complex. Otherwise the right choice is by luck.

Here is a conceptual solution to the problem
Attachments

positive.png
positive.png [ 303.57 KiB | Viewed 2341 times ]

Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1315
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Is x + y > 0 ?  [#permalink]

Show Tags

New post 29 Jan 2017, 02:17
sunita123 wrote:
Is \(x + y > 0\)?

(1) \(x - y > 0\)
(2) \(x^{2} - y^{2} > 0\)


We can rephrase the question by subtracting y from both sides of the inequality: Is \(x > -y\) ?
 
(1) INSUFFICIENT: If we add y to both sides, we see that x is greater than y. We can use numbers here to show that this does not necessarily mean that \(x > -y\). If \(x = 4\) and \(y = 3\), then it is true that \(x\) is also greater than \(-y\). However if \(x = 4\) and \(y = -5\), \(x\) is greater than \(y\) but it is NOT greater than \(-y\). 
 
(2) INSUFFICIENT:  If we factor this inequality, we come up \((x + y)(x – y) > 0\). 
For the product of \((x + y)\) and \((x – y)\) to be greater than zero, the must have the same sign, i.e. both negative or both positive. 
This does not help settle the issue of the sign of \(x + y\). 

(1) AND (2) SUFFICIENT: From statement 2 we know that \((x + y)\) and \((x – y)\) must have the same sign, and from statement 1 we know that \((x – y)\) is positive, so it follows that \((x + y)\) must be positive as well.
 
The correct answer is C.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Manager
Manager
avatar
G
Joined: 30 Dec 2016
Posts: 224
Schools: Schulich
GMAT 1: 650 Q42 V37
GPA: 4
WE: Business Development (Other)
Premium Member Reviews Badge
Re: Is x + y > 0 ?  [#permalink]

Show Tags

New post 16 Oct 2017, 01:59
Bunuel wrote:
Is x + y > 0 ?

(1) x - y > 0 --> x > y. One number is greater than another. From this we cannot say whether their sum is positive. Not sufficient.

(2) x^2 - y^2 > 0 --> x^2 > y^2 --> |x| > |y|. One number is further from 0 than another. From this we cannot say whether their sum is positive. Not sufficient.

(1)+(1) From (2) (x - y)(x + y) > 0 (x + y and x - y have the same sign) and from (1) x - y > 0, thus x + y > 0. Sufficient.

Answer: C.


Hi Bunuel

A little help plz.
This is how i did statement 2.
x^2 - y^2 > 0 --> (x+y) (x-y) > 0 --> if we divide both sides by x-y we get x+y > 0
Hence sufficient.
Can you please help me fill gaps in my understanding here ?

Thanks in advance.
_________________

Regards
SandySilva


____________
Please appreciate the efforts by pressing +1 KUDOS (:

GMAT Club Bot
Re: Is x + y > 0 ? &nbs [#permalink] 16 Oct 2017, 01:59
Display posts from previous: Sort by

Is x + y > 0 ?

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


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.