Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Jul 2015, 22:56
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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is a^2 + a > -b^2?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 05 Nov 2010
Posts: 32
Followers: 0

Kudos [?]: 11 [1] , given: 0

Is a^2 + a > -b^2? [#permalink] New post 07 Nov 2010, 12:39
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

52% (02:13) correct 48% (01:18) wrong based on 108 sessions
Is a^2 + a > -b^2?

(1) a^2 + b^2 = 1
(2) a > 0
[Reveal] Spoiler: OA
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28731
Followers: 4577

Kudos [?]: 47204 [2] , given: 7108

Re: a^2+a>-b^2 [#permalink] New post 07 Nov 2010, 13:54
2
This post received
KUDOS
Expert's post
Creeper300 wrote:
a^2+a > -b^2?

1. a^2+ b^2=1
2. a>0


Is \(a^2+b^2>-a\)? or is \(a^2+a+b^2>0\)

(1) \(a^2+b^2=1\) --> is \(1>-a\) or is \(a>-1\), not sufficient. For example if \(a=1\) and \(b=0\) then the answer will be YES but if \(a=-1\) and \(b=0\) then the answer will be NO.

(2) \(a>0\) --> so \(a^2+a+b^2=(positive)+(positive)+(non-negative)\) which is clearly positive, so \(a^2+a+b^2>0\). Sufficient.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 27 Aug 2014
Posts: 76
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)
Followers: 0

Kudos [?]: 30 [0], given: 14

CAT Tests
Is a^2 + a > -b^2? [#permalink] New post 23 Nov 2014, 07:45
Creeper300 wrote:
Is a^2 + a > -b^2?

(1) a^2 + b^2 = 1
(2) a > 0


did it in the following way:

question becomes:
is a^2 + b^2 + a > 0, as the minimum value of a^2 + b^2 is 0, the question is is a> 0?

from statement 1: a^2 + b^2 = 1, which reduces to a> -1, when a = b= 0 then a = 0 and not greater than 0, so NSF
statement 2 directly answers the question, sufficient

[B]
Intern
Intern
avatar
Joined: 28 Dec 2013
Posts: 2
Schools: INSEAD Jan '15
Followers: 0

Kudos [?]: 0 [0], given: 34

Re: Is a^2 + a > -b^2? [#permalink] New post 26 Nov 2014, 18:16
Bunuel wrote:
Creeper300 wrote:
a^2+a > -b^2?

1. a^2+ b^2=1
2. a>0


Is \(a^2+b^2>-a\)? or is \(a^2+a+b^2>0\)

(1) \(a^2+b^2=1\) --> is \(1>-a\) or is \(a>-1\), not sufficient. For example if \(a=1\) and \(b=0\) then the answer will be YES but if \(a=-1\) and \(b=0\) then the answer will be NO.

(2) \(a>0\) --> so \(a^2+a+b^2=(positive)+(positive)+(non-negative)\) which is clearly positive, so \(a^2+a+b^2>0\). Sufficient.

Answer: B.



Hi Bunnel ,

Shouldnt this be D , since statement (1) gives a>-1 ,so a cannot be negative , and both a & b are not zero (a^2 + b^=1).
Manager
Manager
User avatar
Joined: 14 Oct 2014
Posts: 71
Location: United States
GMAT 1: 500 Q36 V23
Followers: 0

Kudos [?]: 39 [0], given: 98

CAT Tests
Is a^2 + a > -b^2? [#permalink] New post 26 Nov 2014, 19:28
Is a^2 + a > -b^2?

Is (a)(a+1) > -b*b?

(1) a^2 + b^2 = 1
a^2 - 1 = - b^2
(a-1)(a+1) = -b^2
Sufficient, because if (a-1)(a+1) = - b* then (a)(a+1) > -b^2

(2) a>0,
Sufficient, because if a>0, then both factors (a) and (a+1) will always be positive satisfying the equation (a)(a+1) > -b^2.

I would guess the answer D?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28731
Followers: 4577

Kudos [?]: 47204 [0], given: 7108

Re: Is a^2 + a > -b^2? [#permalink] New post 27 Nov 2014, 02:14
Expert's post
mattapattu wrote:
Bunuel wrote:
Creeper300 wrote:
a^2+a > -b^2?

1. a^2+ b^2=1
2. a>0


Is \(a^2+b^2>-a\)? or is \(a^2+a+b^2>0\)

(1) \(a^2+b^2=1\) --> is \(1>-a\) or ", not sufficient. For example if \(a=1\) and \(b=0\) then the answer will be YES but if \(a=-1\) and \(b=0\) then the answer will be NO.

(2) \(a>0\) --> so \(a^2+a+b^2=(positive)+(positive)+(non-negative)\) which is clearly positive, so \(a^2+a+b^2>0\). Sufficient.

Answer: B.



Hi Bunnel ,

Shouldnt this be D , since statement (1) gives a>-1 ,so a cannot be negative , and both a & b are not zero (a^2 + b^=1).



You missed a point there.

(1) says that \(a^2+b^2=1\). If we substitute this into the question (is \(a^2+a+b^2>0\)?), the question becomes "is \(a>-1\)?". As shown in the solution it can be more than -1 (a=1 and b=0) as well as equal to -1 (a=-1 and b=0). So, we cannot answer the question with a definite YES or NO. Thus the statement is not sufficient.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28731
Followers: 4577

Kudos [?]: 47204 [0], given: 7108

Re: Is a^2 + a > -b^2? [#permalink] New post 27 Nov 2014, 02:16
Expert's post
1
This post was
BOOKMARKED
viktorija wrote:
Is a^2 + a > -b^2?

Is (a)(a+1) > -b*b?

(1) a^2 + b^2 = 1
a^2 - 1 = - b^2
(a-1)(a+1) = -b^2
Sufficient, because if (a-1)(a+1) = - b* then (a)(a+1) > -b^2

(2) a>0,
Sufficient, because if a>0, then both factors (a) and (a+1) will always be positive satisfying the equation (a)(a+1) > -b^2.

I would guess the answer D?


The red part is not correct. Consider a=-1 and b=0. The correct answer is B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Re: Is a^2 + a > -b^2?   [#permalink] 27 Nov 2014, 02:16
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Is the value of a^2 - b^2 > greater than the value of carcass 5 29 Sep 2012, 11:21
1 Experts publish their posts in the topic Is a^2 + b^2 > c^2 metallicafan 2 19 Jun 2012, 11:18
4 Is a^2 + b^2 > c^2? metallicafan 6 27 Dec 2011, 09:12
Experts publish their posts in the topic Is a^2 + b^2 > c^2? metallicafan 1 24 Nov 2011, 06:43
Experts publish their posts in the topic Is a^2 + b^2 > c^2 ? tirupatibalaji 8 06 Jan 2011, 03:06
Display posts from previous: Sort by

Is a^2 + a > -b^2?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.