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# is 1/p > r/(r^2 + 2) ? 1. r=p 2. r>0 why isn't first

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is 1/p > r/(r^2 + 2) ? 1. r=p 2. r>0 why isn't first [#permalink]  01 Nov 2007, 20:56
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is 1/p > r/(r^2 + 2) ?

1. r=p
2. r>0

why isn't first statement enough...please explain.
VP
Joined: 08 Jun 2005
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is 1/p > r/(r^2 + 2)

Statement 1

r=p

1/r > r/(r^2 + 2)

this is insufficient because you are assuming that r > 0 ---> then:

r^2+2 > r^2

if r < 0 then

r^2+2 < r^2

insufficient

Statement 2

state that r > 0

insufficient

both Statements

sufficient

Last edited by KillerSquirrel on 01 Nov 2007, 22:25, edited 1 time in total.
Director
Joined: 03 Sep 2006
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KillerSquirrel wrote:
is 1/p > r/(r^2 + 2)

Statement 1

r=p

1/r > r/(r^2 + 2)

this is insufficient because you are assuming that (r^2 + 2) > 0 ---> then:

r^2+2 > r^2

if (r^2 + 2) < 0 then

r^2+2 <r> 0

insufficient

:)

Hi squirrel,

Can you give any example in which (r^2 + 2) < 0???

r^2 is always positive, whether r is positive, negative or fraction.

Thus statement (1) should be sufficient.

VP
Joined: 08 Jun 2005
Posts: 1147
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LM wrote:
KillerSquirrel wrote:
is 1/p > r/(r^2 + 2)

Statement 1

r=p

1/r > r/(r^2 + 2)

this is insufficient because you are assuming that (r^2 + 2) > 0 ---> then:

r^2+2 > r^2

if (r^2 + 2) < 0 then

r^2+2 <r> 0

insufficient

Hi squirrel,

Can you give any example in which (r^2 + 2) < 0???

r^2 is always positive, whether r is positive, negative or fraction.

Thus statement (1) should be sufficient.

(r^2 + 2) cannot be less then 0 but r can - you multiply r*(r^2+2) both sides of the equation !

thanks for the heads up ! I will correct my post, the answer is still (C)

Director
Joined: 03 Sep 2006
Posts: 885
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Kudos [?]: 254 [0], given: 33

KillerSquirrel wrote:
LM wrote:
KillerSquirrel wrote:
is 1/p > r/(r^2 + 2)

Statement 1

r=p

1/r > r/(r^2 + 2)

this is insufficient because you are assuming that (r^2 + 2) > 0 ---> then:

r^2+2 > r^2

if (r^2 + 2) < 0 then

r^2+2 <r> 0

insufficient

:)

Hi squirrel,

Can you give any example in which (r^2 + 2) < 0???

r^2 is always positive, whether r is positive, negative or fraction.

Thus statement (1) should be sufficient.

(r^2 + 2) cannot be less then 0 but r can - you multiply r*(r^2+2) both sides of the equation !

thanks for the heads up ! I will correct my post, the answer is still (C)

:)

But you don't have to multiply both sides with "r".

The equation is r^2 + 2 > r^2
Intern
Joined: 06 Aug 2007
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Hi squirrel, Thanks for your explanation.
I still second LM's point. why should we consider multiplying any positive expression with a negative variable ?
SVP
Joined: 01 May 2006
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(C) as well

is 1/p > r/(r^2 + 2) ?
<=> (r^2+2)/p > r ? as r^2 + 2 > 0

Stat1
p=r

implies that (r^2+2)/p = (r^2+2)/r = r + 2/r

r + 2/r > r only if 2/r >0 and so r > 0.

INSUFF.

Stat2
r > 0 : p can be anything...

INSUFF.

Both 1 and 2
Bingo... We know have r > 0.... So r + 2/r > r <=> 1/p > r/(r^2 + 2)

SUFF.
VP
Joined: 28 Mar 2006
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LM wrote:
KillerSquirrel wrote:
LM wrote:
KillerSquirrel wrote:
is 1/p > r/(r^2 + 2)

Statement 1

r=p

1/r > r/(r^2 + 2)

this is insufficient because you are assuming that (r^2 + 2) > 0 ---> then:

r^2+2 > r^2

if (r^2 + 2) < 0 then

r^2+2 <r> 0

insufficient

Hi squirrel,

Can you give any example in which (r^2 + 2) < 0???

r^2 is always positive, whether r is positive, negative or fraction.

Thus statement (1) should be sufficient.

(r^2 + 2) cannot be less then 0 but r can - you multiply r*(r^2+2) both sides of the equation !

thanks for the heads up ! I will correct my post, the answer is still (C)

But you don't have to multiply both sides with "r".

The equation is r^2 + 2 > r^2

how do you know the sign of r??

if r>1/r it doesnt mean r^2>1

simply because the equation changes as per the sign of r.
Senior Manager
Joined: 18 Jun 2007
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Fig wrote:
(C) as well

is 1/p > r/(r^2 + 2) ?
<r> r ? as r^2 + 2 > 0

Stat1
p=r

implies that (r^2+2)/p = (r^2+2)/r = r + 2/r

r + 2/r > r only if 2/r >0 and so r > 0.

INSUFF.

Stat2
r > 0 : p can be anything...

INSUFF.

Both 1 and 2
Bingo... We know have r > 0.... So r + 2/r > r <1> r/(r^2 + 2)

SUFF.

Good explanation Fig.
Problem with equation like 1/r> r/r2+2 is that one can get tempt to go for full - r^2 + 2 = r^2- but the best way to solve this to stop at r^2 + 2 / r = r.With this answer become clear.
Manager
Joined: 22 Oct 2006
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My Take is C. But I worked out in a different way.

1. Is not sufficient because, when r=p, it appears to be sufficient but what if r=p=0? Hence, in my view it is not sufficient

2. Not sufficient

Together makes sense.

Do you agree?
Intern
Joined: 06 Aug 2007
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appuvar wrote:
My Take is C. But I worked out in a different way.

1. Is not sufficient because, when r=p, it appears to be sufficient but what if r=p=0? Hence, in my view it is not sufficient

2. Not sufficient

Together makes sense.

Do you agree?

Sounds reasonable, at least I can't deny it.
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