variables

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

A) p=r
B) r>0

[cramya]

It should be C)

[cramya]

Is 1/p > r/r^2+2

Stmt I

p=r

Is 1/r > r/r^2+1

If r=-1/2 NO
If r= 1/2 then YES

insuff

Stmt II

r>0

No info about p which tell us this statement is also insufficeint yes/no answers possible based on various values of r and p

Stmt I and II together

Is 1/r > r/r^2+2

Since r>0 we can safely cross multiply both sides of inequalitiy without affecting the existing inequality

Is 1/r > r/r^2+2

Is r^2+2 > r^2

YES

SUFF

Choose C)

[vittalgmat]

From the Q stem asks
1/p - r/(r^2 +2) > 0 ?

Stmt 1.

substitute p =r and get the expression in terms of r.
LHS of the Q stem is
1/r - r/(r^2+2)

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

-> 2/(r^3 +2r)

not sufficient coz we dont know r.


Stmt 2.
r > 0
not sufficient .. coz dont know p .

combining.
No matter what # u choose for r the value of the expression is always > 0

As an aside.
lim, r -> 0 2/r^3 +2r = + infinity which is >0
lim, r -> +infinity, 2/(r^3 +2r) = 0
(here since the expression reaches 0 only at infinity, we can assume for all practical purposes, value of expr is > 0).

Hence C.

HT Helps

[ronniecoleman]

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

A) p=r
B) r>0

1)

p = r

1/p = 1/r

1/p = r/r*r

1/p > r/r*r + 2 ( if r > 0 )

1/p < r/r*r+2 ( if r < 0)

Insuff

1) r > 0

does not help

Together both helps

IMO C

[dario.brignone]

Hi,

I also get C) but with different method, could someone confirm whether it's correct.

I simplified the inequality in the statement:
1/p > r/(r^2+2)
1/p - r/(r^2+2) > 0
(r^2+2-rp)/(p(r^2+2)) > 0
(r(r-p)+2)/(p(r^2+2)) > 0

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2)
we only know that r/(r^2+2) is positive, nothing else -> INSUFFICIENT

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1)
p=r, hence the above simplify to:
2/(p(r^2+2)) > 0
as (r^2+2) is always positive, then 2/(p(r^2+2)) > 0 is positive if p is positive, we don't know it -> INSUFFICIENT

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1)+2)
we have (r(r-p)+2)/(p(r^2+2)) > 0
knowing that p=r we can simplify: 2/(p(r^2+2)) > 0
if p=r and r>0 -> p>0
if p>0 then 2/(p(r^2+2)) > 0 is positive -> SUFFICIENT