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

 It is currently 07 Jul 2015, 18:57

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Director
Joined: 27 Jun 2005
Posts: 513
Location: MS
Followers: 2

Kudos [?]: 37 [0], given: 0

What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink]  16 Feb 2006, 22:23
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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
Intern
Joined: 06 Jan 2006
Posts: 23
Location: Illinois
Followers: 0

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

B? I hate inequalities... 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?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 195 [0], given: 0

(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)
Intern
Joined: 06 Jan 2006
Posts: 23
Location: Illinois
Followers: 0

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

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.....
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 195 [0], given: 0

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.
SVP
Joined: 03 Jan 2005
Posts: 2246
Followers: 13

Kudos [?]: 226 [0], given: 0

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.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

SVP
Joined: 03 Jan 2005
Posts: 2246
Followers: 13

Kudos [?]: 226 [0], given: 0

cattalk wrote:
B? I hate inequalities... 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.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 7

Kudos [?]: 37 [0], given: 0

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.
Manager
Joined: 16 Sep 2005
Posts: 62
Followers: 1

Kudos [?]: 2 [0], given: 0

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.
_________________

Thanks

Director
Joined: 27 Jun 2005
Posts: 513
Location: MS
Followers: 2

Kudos [?]: 37 [0], given: 0

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
SVP
Joined: 03 Jan 2005
Posts: 2246
Followers: 13

Kudos [?]: 226 [0], given: 0

(-5/2)^2-5/2-(3/4) = 3 not -3.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Director
Joined: 27 Jun 2005
Posts: 513
Location: MS
Followers: 2

Kudos [?]: 37 [0], given: 0

Oppp!!
thanx HongHu
VP
Joined: 20 Sep 2005
Posts: 1021
Followers: 3

Kudos [?]: 27 [0], given: 0

Solving the inequality we get the range as

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

z < -3/2 or z > 1/2. Thus, the minimum value is when z = -3/2....B.
Similar topics Replies Last post
Similar
Topics:
4 If x > 0, what is the least possible value for x + 1/x ? 4 20 Oct 2014, 06:09
8 If x > 0.9, which of the following could be the value of x? 9 11 Sep 2014, 18:42
8 If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of 3 16 Apr 2013, 05:07
9 Which of the following is a value of x for which x^11-x^3>0 9 27 Jan 2012, 11:58
What is the minimum value of z for which (z^2)+z-(3/4)>0 21 18 Oct 2005, 20:46
Display posts from previous: Sort by

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

 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®.