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

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What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink]  18 Oct 2005, 20:46
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65% (hard)

Question Stats:

55% (02:46) correct 45% (01:35) wrong based on 58 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
[Reveal] Spoiler: OA
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[#permalink]  18 Oct 2005, 20:49
Equation can be written as:
4z^2 + 4z - 3 > 0
(2z-1)(2z+3)>0
Limits: z < -3/2 or z>1/2

Ans: A
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[#permalink]  18 Oct 2005, 21:02
That was rather a quick reply, thanx. I'll post the OA as and when i get some more replies. However, I have just a couple of questions

1) Why do we not sovle this problem by simply backsolving and determining the option which returns the least value using the equation? Why are you finding out the range?

2) In your solution, why have u changed the inequality sign in "z<-3/2" ?
ie. shouldng it be z>-3/2 or z>1/2 ?...but even then this range doesnt make sense.

3) One question regarding how to use this forum more effectively: how do i set an email alert when i wish to track all the replies that are posted to this question. There is an option "Notify me when a reply is posted". But i am notified when i get only one reply!

Thanks.
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Re: PS - Value of z [#permalink]  18 Oct 2005, 21:10
(C) -1/2. C doesnot give the value of (z^2)+z-(3/4)>0.
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[#permalink]  18 Oct 2005, 21:17
we do not have to find a value where "LHS > 0 is not true". ie. LHS < 0. Coz in that case, (B) and (E) too give a value lesser than 0
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[#permalink]  19 Oct 2005, 07:30
I think B -3/2 is the best ans...

just like ywilfred factor, but remember you cant pick a value for which

(2z-1)(2z-3) are both negative...so -3/2 is the only value for which the expression =0 and therefore it is not > 0.....
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[#permalink]  19 Oct 2005, 07:51
Your right, the OA is B
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[#permalink]  19 Oct 2005, 09:02
ywilfred wrote:
Equation can be written as:
4z^2 + 4z - 3 > 0
(2z-1)(2z+3)>0
Limits: z < -3/2 or z>1/2

Ans: A

you calculated the right answer - you got it right in my book.
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Re: PS - Value of z [#permalink]  19 Oct 2005, 09:50
cdaat wrote:
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

z^+z-3/4=(z+1/2)^2-1
It>0 is not true means it has to be less or equal to 0.
(z+1/2)^2-1<=0
(z+1/2)^2<=1
-1<=z+1/2<=1
-3/2<=z<=1/2
The minimum value of z is thus -3/2.
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Last edited by HongHu on 19 Oct 2005, 09:58, edited 1 time in total.
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[#permalink]  19 Oct 2005, 09:58
Yes. I often make such errors, oops. Let it be an example for you not to do it in the real test.
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[#permalink]  19 Oct 2005, 10:05
I went about solving the problem a little different.

Because the question asked for the least values I decided to plug in the second least value and solve. I would have adjusted my next value based on the answer i received. Because i got =0. I didnt' go any further.

It isn't very technical but it made it quick to solve.
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[#permalink]  19 Oct 2005, 10:05
HongHu wrote:
Yes. I often make such errors, oops. Let it be an example for you not to do it in the real test.

Unfortunately Mr. Honghu such errors are the bane of my existence.
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Re: PS - Value of z [#permalink]  19 Oct 2005, 14:47
cdaat wrote:
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

we have to find z so that (z^2)+z-(3/4)>=0
or (z+3/2)(z-1/2)<=0, or 1/2<=z<=3/2, Thus z=1/2 . E is the answer
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[#permalink]  19 Oct 2005, 16:59
Titleist wrote:
HongHu wrote:
Yes. I often make such errors, oops. Let it be an example for you not to do it in the real test.

Unfortunately Mr. Honghu such errors are the bane of my existence.

hmmm.... Are you sure Honghu is Mr.?
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[#permalink]  19 Oct 2005, 18:21
HIMALAYA wrote:
Titleist wrote:
HongHu wrote:
Yes. I often make such errors, oops. Let it be an example for you not to do it in the real test.

Unfortunately Mr. Honghu such errors are the bane of my existence.

hmmm.... Are you sure Honghu is Mr.?

It's 'Ms.' !
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[#permalink]  19 Oct 2005, 22:15
ywilfred wrote:
HIMALAYA wrote:
Titleist wrote:
HongHu wrote:
Yes. I often make such errors, oops. Let it be an example for you not to do it in the real test.

Unfortunately Mr. Honghu such errors are the bane of my existence.

hmmm.... Are you sure Honghu is Mr.?

It's 'Ms.' !

Oops! My bad. A thousand apologies Ms. Honghu. Apparently, my data sufficiency skills for real life situations has not kept pace with the gmat.
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[#permalink]  19 Oct 2005, 22:23
lp54 wrote:
I went about solving the problem a little different.

Because the question asked for the least values I decided to plug in the second least value and solve. I would have adjusted my next value based on the answer i received. Because i got =0. I didnt' go any further.

It isn't very technical but it made it quick to solve.

agree, this one is ok and not too complicated, you can definitely plug and play
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[#permalink]  20 Oct 2005, 08:17
Titleist wrote:
ywilfred wrote:
HIMALAYA wrote:
Titleist wrote:
HongHu wrote:
Yes. I often make such errors, oops. Let it be an example for you not to do it in the real test.

Unfortunately Mr. Honghu such errors are the bane of my existence.

hmmm.... Are you sure Honghu is Mr.?

It's 'Ms.' !

Oops! My bad. A thousand apologies Ms. Honghu. Apparently, my data sufficiency skills for real life situations has not kept pace with the gmat.

Heh maybe I'm just a Mr HongHu pretending to be a Ms HongHu so that my mistakes are more easily tolerated ... Isn't real life more interesting and complicated.
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keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

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Algebra [#permalink]  28 Oct 2011, 10:41
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

Can someone please explain how to solve this question. Saw it on a Kaplan practice exam.

Thank you!
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Re: What is the minimum value of z for which z^2+z-3/4>0 [#permalink]  29 Oct 2011, 01:03
On solving the equation we get (2z+3)(2z-1)>0.
The critical points for the above equation will be -3/2 and 1/2 (where value of z=0).

Now let us find put 3 no's in the equation- 2 which lie on either side of the critical points and 1 in between.

Lets say -2,0 and 2.
*On filling -2 in the equation we get 5/4 which is +ve.(no number within this range (-infinity to -3/4) will satisfy the condition as they all will be more than 0)

*On filling 0 in the equation we get -3/4 which is -ve

*On filling 2 we get 21/4 which is +ve.(no number within this range (1/2 to +infinity) will satisfy the condition as they all will be more than 0)

We can safely eliminate a and c options.

Now at -3/2 and 1/2 we know value is 0. Let us check at 1/4. Value at 1/4 = -9/16 = -0.56.

Question clearly says minimum value of z where equation>0 is not true. so it means value can be 0 or less than 0. We need to find the minimum value of z and not of the equation where the condition holds.
out of -3/2,1/4 and 1/2 minimum value where the condition will not be true is -3/2.
Hence option b.

Hope it helps...
Re: What is the minimum value of z for which z^2+z-3/4>0   [#permalink] 29 Oct 2011, 01:03

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

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