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

It is currently 18 Jun 2018, 02:57

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

If b<0, is 5b(a+b)>-a^2-b^2? 1) a+2b>0 2) a+3b>0

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

Hide Tags

Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1285
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
If b<0, is 5b(a+b)>-a^2-b^2? 1) a+2b>0 2) a+3b>0 [#permalink]

Show Tags

New post 09 Mar 2017, 22:30
1
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

28% (02:16) correct 72% (01:44) wrong based on 46 sessions

HideShow timer Statistics

If \(b<0\), is \(5b(a+b)>-a^2-b^2\)? 

1) \(a+2b>0\)

2) \(a+3b>0\)

_________________

"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!

1 KUDOS received
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1285
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Re: If b<0, is 5b(a+b)>-a^2-b^2? 1) a+2b>0 2) a+3b>0 [#permalink]

Show Tags

New post 03 Apr 2017, 16:48
1
1
ziyuen wrote:
If \(b<0\), is \(5b(a+b)>-a^2-b^2\)? 

1) \(a+2b>0\)

2) \(a+3b>0\)


OFFICIAL EXPLANATION


You need preliminary knowledge to solve this question.

If b<0, you get -3b>-2b>-b. If you take the 1st step of the variable approach and modify the original condition and the question,
Que: is 5b(a+b) > -a^2-b^2 → 5ab+5b2+a^2+b^2>0, a^2+5ab+6b^2>0, or (a+3b)(a+2b)>0

In the original condition, there are 2 variables (a, b) and 1 equation (b<0), and in order to match the number of variables to the number of equations, there must be 1 more equation. Therefore, D is most likely to be the answer.

In the case of con 1), a>-2b, so (a, b) = (3,-1) no, and (a, b) = (5,-1) yes, hence it is not sufficient.

In the case of con 2), a>-3b>-2b. This is because b<0, and it is shown in the preliminary knowledge above. If so, a>-3b and a>-2b, then a+3b>0 and a+2b>0. Since (a+3b)(a+2b)>0 is always yes, it is sufficient. The answer is B.
_________________

"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!

Intern
Intern
avatar
Joined: 10 Jan 2017
Posts: 6
Re: If b<0, is 5b(a+b)>-a^2-b^2? 1) a+2b>0 2) a+3b>0 [#permalink]

Show Tags

New post 04 Apr 2017, 01:29
Can someone explain this more easily? Don't get it at all.
Manager
Manager
avatar
S
Joined: 25 Apr 2016
Posts: 57
If b<0, is 5b(a+b)>-a^2-b^2? 1) a+2b>0 2) a+3b>0 [#permalink]

Show Tags

New post 04 Apr 2017, 01:51
after factorizing the inequality would boils down to (2b+a)(a+3b)>0 and as "b"<0, the solution for the inequality would be a>-2b or a<-3b. Try consider b=-1, now, the 1st statement says a>-2 and that to me is sufficient and not to mention that 2nd statement would clearly be ambiguous as the solution suggest. -> for me it's A
If b<0, is 5b(a+b)>-a^2-b^2? 1) a+2b>0 2) a+3b>0   [#permalink] 04 Apr 2017, 01:51
Display posts from previous: Sort by

If b<0, is 5b(a+b)>-a^2-b^2? 1) a+2b>0 2) a+3b>0

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


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®.