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# If z┬▓ - 4z > 5 then which of the following

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Manager
Joined: 27 Jul 2003
Posts: 122
Location: Singapore
If zâ”¬â–“ - 4z > 5 then which of the following [#permalink]

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15 Oct 2003, 01:31
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If z┬▓ - 4z > 5 then which of the following is always true

A) z > -5

B) z < 5

C) z > -1

D) z < 1

E) z < -1
CEO
Joined: 15 Aug 2003
Posts: 3454
Re: PS: Which of the following? [#permalink]

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15 Oct 2003, 01:46
araspai wrote:
If z┬▓ - 4z > 5 then which of the following is always true

A) z > -5

B) z < 5

C) z > -1

D) z < 1

E) z < -1

(z-5) ( z+1 ) > 0

1.
z-5 >0 AND z +1 >0

z > 5 AND z>-1

2.
z-5 < 0 AND z +1 < 0

Z < 5 AND z<-1

1. either Z > 5 or Z<-1 is always true.

of them, only Z<-1 is there...Answer E
SVP
Joined: 30 Oct 2003
Posts: 1790
Location: NewJersey USA

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29 Dec 2003, 19:52
I did not understand you explaination at all.
SVP
Joined: 30 Oct 2003
Posts: 1790
Location: NewJersey USA

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29 Dec 2003, 19:55
I did not understand you explaination at all.

if Z > 5 then Z is always > -1

if Z < -1 then Z is always < 5

so you choose the smallest value Z < -1 ?
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4288

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29 Dec 2003, 20:33
z^2 - 4z > 5
z^2 - 4z - 5 > 0
(z+1)(z-5) > 0

Try plugging in values knowing that the treshold values are -1 and 5 and you will see that the condition will hold true whenever you have values for z larger than 5 or less than -1
_________________

Best Regards,

Paul

Intern
Joined: 17 Aug 2003
Posts: 38
Location: USA
Re: PS: Which of the following? [#permalink]

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30 Dec 2003, 08:20
praetorian123 wrote:
araspai wrote:
If z┬▓ - 4z > 5 then which of the following is always true

A) z > -5

B) z < 5

C) z > -1

D) z < 1

E) z < -1

(z-5) ( z+1 ) > 0

1.
z-5 >0 AND z +1 >0

z > 5 AND z>-1

2.
z-5 < 0 AND z +1 < 0

Z < 5 AND z<-1

1. either Z > 5 or Z<-1 is always true.

of them, only Z<-1 is there...Answer E

praetorian123 can you please explain this. What are the rules for handling quads with inequalities? From your answer it looks like you just factor as normal but apply > and < to the two possible outcomes. Is this correct?

If so how did you get to this part?

1. either Z > 5 or Z<-1 is always true.

how about Z<5 or Z>-1 how did you eliminate these.

It's probably something simple but i can't see it.

Thanks
Re: PS: Which of the following?   [#permalink] 30 Dec 2003, 08:20
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