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# There is some flaw in my logic here...pls point it out....

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Intern
Joined: 15 Aug 2003
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Location: California
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There is some flaw in my logic here...pls point it out.... [#permalink]  11 Sep 2003, 08:02
There is some flaw in my logic here...pls point it out....
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

I solve it as...

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

(z - 5) > 0 and (z +1) > 0 => z > 5 and z < -1

OR

(z - 5) < 0 and (z +1) < 0 => z <5 and z>-1

So why is the answer E?
Intern
Joined: 21 Jul 2003
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easy way to see it [#permalink]  11 Sep 2003, 10:34
an easier way to see it would be to use a number line:

you are given: (Z^2)-4Z>5

so you eventually get (z-5) (z+1) > 0 , but this is not the solution set:

you can see it better drawn on a number line:

(z-5)=0 => z=5 put this on a number line
(z+1)=0 => z=-1 put this on a number line

so now you have split a number line into three sections:

etc... -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 etc...

(sorry best way i thought of to replicate a number line:)

from here just plug in numbers from the three "sections" into your original equation (z^2)-4Z-5>0 and see if it holds true (once is enough)

plug in something less than -1 (try -2 and you get 12-5>0 yes!!)
plug in something in the middle (try 0 and get -5>0 NO!!)
plug in something above 5 (try 6 and get 36-29>0 Yes!!)

but only X<-1 is one of the answer choices ...so there it is...i hope you can "see" it better this way...
CEO
Joined: 15 Aug 2003
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Re: WHAT IS THE BUG ??? [#permalink]  11 Sep 2003, 17:52
neetamittal wrote:
There is some flaw in my logic here...pls point it out....
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

I solve it as...

(z - 5) (z +1) > 0
(z - 5) > 0 and (z +1) > 0 => z > 5 and z < -1
OR

(z - 5) < 0 and (z +1) < 0 => z <5 andz>-1So why is the answer E?

Hey Neeta

See the bold part in your analysis..

z+1 > 0 .... so z > -1 ...
z +1 < 0 .... so z < -1 ...

Nuances..thats what get us most of the time

So for the first condition.... z > 5 is always true

and for the second condition.... z <-1 is always true..

i see only z < -1 in the answer choices

The final check :
I would plug two three # 's less than -1 ..like -5 ,-10 , -15...and see whether the inequality holds..

Thanks
Praetorian
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Joined: 30 Oct 2003
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Location: NewJersey USA
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Even easier way

If z┬▓ - 4z > 5 then which of the following is always true
A) z > -5 ( make z = 0 as 0 > -5 ) false
B) z < 5 ( make z = 0 as 0 < 5 ) false
C) z > -1 ( make z = 0 as 0 > -1 ) false
D) z < 1 ( make z = 0 as z < 1 ) false
E) z < -1 ( z cannot be 0 if z = -1 then 1+4 = 5 so if z < -1 then
the condition is always true )
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