NEW HERE? LEARN MORE
closeclose
Last visit was: 29 Apr 2024, 03:32 It is currently 29 Apr 2024, 03:32
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the minimum value of z for which (z^2)+z-(3/4)>0

User avatar
cool_jonny009
Manager
Manager
Joined: 27 Jun 2005
Posts: 241
Own Kudos [?]: 2102 [0]
Given Kudos: 0
Location: MS
Send PM
What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   16 Feb 2006, 23:23
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
Hide Show timer Statistics
What is the minimum value of z for which (z^2)+z-(3/4)>0 is not true?

(A) -5/2
(B) -3/2
(C) -1/2
(D) 1/4
(E) 1/2



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
cattalk
Intern
Intern
Joined: 06 Jan 2006
Posts: 20
Own Kudos [?]: [0]
Given Kudos: 0
Location: Illinois
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   16 Feb 2006, 23:29
B? I hate inequalities...:evil: I always end up spending too much time on them. What is a good way of finding the answer without plugging in all the numbers?
User avatar
ywilfred
SVP
SVP
Joined: 07 Jul 2004
Posts: 2004
Own Kudos [?]: 1900 [0]
Given Kudos: 0
Location: Singapore
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   16 Feb 2006, 23:36
(z^2)+z-(3/4) = 4z^2 + 4z - 3 > 0
(2z+3)(2z-1) > 0
z>0.5

Smallest value for it not to be true = 1/2

since (2z+3)(2z-1) = 0 (and so not >0)
User avatar
cattalk
Intern
Intern
Joined: 06 Jan 2006
Posts: 20
Own Kudos [?]: [0]
Given Kudos: 0
Location: Illinois
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   16 Feb 2006, 23:49
Wilfred wouldn't it still be B though since z=-3/2 satisfies 2z+3=0 ?
Good idea multiplying both sides by 4, I gave up thinking it was too complicate to factor..... :oops:
User avatar
ywilfred
SVP
SVP
Joined: 07 Jul 2004
Posts: 2004
Own Kudos [?]: 1900 [0]
Given Kudos: 0
Location: Singapore
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   17 Feb 2006, 01:30
For (z^2)+z-(3/4)>0, we need z > 0.5. I took the meaning of minimum value as z=0.5. That's sufficient to fail the inequality.
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 769 [0]
Given Kudos: 0
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   17 Feb 2006, 07:24
The question should be interpreted as this: What is the minimum value of z for which (z^2)+z-(3/4) <= 0 is true?

This is equivalent to (2z+3)(2z-1) <= 0
The solution set is -3/2<=z<=1/2
So the minimal value for z is -3/2.
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 769 [0]
Given Kudos: 0
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   17 Feb 2006, 07:30
cattalk wrote:
B? I hate inequalities...:evil: I always end up spending too much time on them. What is a good way of finding the answer without plugging in all the numbers?


Seems that you have a pretty good grasp already. The best way for this kind of questions is to solve the inequality. You could look at this post although it only talks the very basic principles.
User avatar
Professor
Director
Director
Joined: 29 Dec 2005
Posts: 566
Own Kudos [?]: 176 [0]
Given Kudos: 0
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   17 Feb 2006, 08:12
if z =-3/2, z^2+z-(3/4) = 9/4-3/2-3/4 = (9-6-3)/4=0
if z =1/2, z^2+z-(3/4) = 1/4 + 1/2 - 3/4 = (1+2-3)/4=0
if z =1/4, z^2+z-(3/4) = 1/16 + 1/4 - 3/4 = (1+4-12)/16=-7/16 so this is not true.

seems -3/2.
User avatar
MBAHopeful
Intern
Intern
Joined: 16 Sep 2005
Posts: 34
Own Kudos [?]: 6 [0]
Given Kudos: 0
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   17 Feb 2006, 11:33
HongHu wrote:
The question should be interpreted as this: What is the minimum value of z for which (z^2)+z-(3/4) <= 0 is true?

This is equivalent to (2z+3)(2z-1) <= 0
The solution set is -3/2<=z<=1/2
So the minimal value for z is -3/2.


B for me too. Honored to know that at least this time my method to approach this problem was similar to HongHu.
User avatar
cool_jonny009
Manager
Manager
Joined: 27 Jun 2005
Posts: 241
Own Kudos [?]: 2102 [0]
Given Kudos: 0
Location: MS
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   17 Feb 2006, 11:56
all right guys the OA is B (-3/2).

But when z =-5/2

(z^2)+z-(3/4)>0 is not True

(-5/2)^2-5/2-(3/4) = -3 (So the inequality is not true ) also -5/2 is smaller than -3/2

this question is from Quant Sticky ...Some body pls explain what i am doing wrong here
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 769 [0]
Given Kudos: 0
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   17 Feb 2006, 13:09
(-5/2)^2-5/2-(3/4) = 3 not -3. :)
User avatar
cool_jonny009
Manager
Manager
Joined: 27 Jun 2005
Posts: 241
Own Kudos [?]: 2102 [0]
Given Kudos: 0
Location: MS
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   18 Feb 2006, 17:29
Oppp!! :oops: :oops:
thanx HongHu
User avatar
lhotseface
Director
Director
Joined: 20 Sep 2005
Posts: 799
Own Kudos [?]: 52 [0]
Given Kudos: 0
Send PM
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink] New post   18 Feb 2006, 20:24
Solving the inequality we get the range as

(2z-1)(2z+3) > 0


z 1/2. Thus, the minimum value is when z = -3/2....B.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink]
18 Feb 2006, 20:24
Moderators:
Bunuel
Math Expert
92990 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions