Author
Message
TAGS:
Manager

Joined: 12 Apr 2006

Posts: 220

Location: India

Followers: 1

Kudos [? ]:
18
[0 ] , given: 17

DS: Is 1/p > r/(r^2+2) [#permalink ]
05 Jul 2006, 20:38

1

This post was BOOKMARKED

Question Stats:

58% (01:57) correct

42% (00:46) wrong

based on 31 sessions
Is 1/p > r/(r^2+2)

1) p = r

2) r > 0

Please explain the answer

VP

Joined: 25 Nov 2004

Posts: 1498

Followers: 6

Kudos [? ]:
27
[0 ] , given: 0

Re: DS: Is 1/p > r/(r^2+2) [#permalink ]
05 Jul 2006, 20:54

humans wrote:

Is 1/p > r/(r^2+2) 1) p = r 2) r > 0 Please explain the answer

from 1, if p=r> -ve, 1/p < r / (r^2+2)

if 0<p=r, 1/p > r / (r^2+2). so insuffcient..

from 2, r>0 is also insuffcient.

togather 1/p > r / (r^2+2).

so C.

SVP

Joined: 30 Mar 2006

Posts: 1741

Followers: 1

Kudos [? ]:
25
[0 ] , given: 0

Will go with C
1) p = r
When p=r=+ve, it satisfies the equation
But when p=r=-ve , the equation fails hence Insuff
2) r>0
P can be anything hence Insuff
Together
p=r=+ve
Hence
1/p > r/(r^2+2)

Director

Joined: 08 Jun 2004

Posts: 502

Location: Europe

Followers: 1

Kudos [? ]:
10
[0 ] , given: 0

Yes 'C' it is.
We must be sure that r and p are both +ve or -ve.

CEO

Joined: 20 Nov 2005

Posts: 2922

Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

Followers: 15

Kudos [? ]:
79
[0 ] , given: 0

C

St1: Fails for -ve fraction values. Pass for all other values.: INSUFF

St2: we don't know about p: INSUFF

Combined: From st1, it was failing for only -ve fraction values of p (or r) but st2 removes that condition. : SUFF

_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Director

Joined: 03 Sep 2006

Posts: 893

Followers: 6

Kudos [? ]:
108
[0 ] , given: 33

DS-prep (1/p > r/(r^2+2) ?) [#permalink ]
23 Jun 2007, 23:40

Pl exp.

Attachments

untitled.PNG [ 68.39 KiB | Viewed 2511 times ]

SVP

Joined: 01 May 2006

Posts: 1816

Followers: 8

Kudos [? ]:
87
[0 ] , given: 0

(C) for me

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

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

From 1
p=r

So,

1/p - r/(r^2+2)

= 1/r - r/(r^2+2)

= [(r^2+2) - r^2] / [r*(r^2+2)]

= 2 / [r*(r^2+2)]

= 1/r * 2/(r^2+2)

As, r^2 >=0, we know that r^2 + 2>= 2 > 0

So, 1/p - r/(r^2+2) > 0 if and only if r > 0. But we do not know if r > 0.

INSUFF.

From 2
r > 0 and nothing about p.

INSUFF.

Both 1 & 2
We have the condition r > 0 for the statment 1 to be concluded.

SUFF.

Intern

Joined: 23 Feb 2010

Posts: 19

Followers: 0

Kudos [? ]:
0
[0 ] , given: 4

Is 1/p > r/(r^2 +2) [#permalink ]
17 Apr 2011, 09:42

Is 1/p > r/(r^2 + 2)? 1. p = r 2. r > 0

Math Forum Moderator

Joined: 20 Dec 2010

Posts: 2048

Followers: 128

Kudos [? ]:
899
[0 ] , given: 376

Re: Is 1/p > r/(r^2 +2) [#permalink ]
17 Apr 2011, 10:02

junior wrote:

Is 1/p > r/(r^2 + 2)? 1. p = r 2. r > 0

Is

\frac{1}{p} > \frac{r}{r^2+2} ?

1. p=r

\frac{1}{r} > \frac{r}{r^2+2} \frac{r^2+2}{r} > r r+\frac{2}{r} > r Is

\frac{2}{r} > 0 We don't know sign of r.

Not Sufficient.

2. r > 0

We don't know anything about p.

Not Sufficient.

Combining both;

We know

\frac{2}{r} > 0 as

r>0 Sufficient.

Ans: "C"

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

Intern

Status: Life.. Be Kind to me

Joined: 12 Jan 2011

Posts: 20

Location: India

GMAT 1 : Q V

WE: Engineering (Telecommunications)

Followers: 0

Kudos [? ]:
6
[0 ] , given: 35

Re: Is 1/p > r/(r^2 +2) [#permalink ]
17 Apr 2011, 11:33

Please tell me what is wrong with my approach1/p > r/(r^2+2) r^2+2-pr>0 when p=rr^2-(r*r)+2=2 which is >0

Math Forum Moderator

Joined: 20 Dec 2010

Posts: 2048

Followers: 128

Kudos [? ]:
899
[1 ] , given: 376

Re: Is 1/p > r/(r^2 +2) [#permalink ]
17 Apr 2011, 12:15
1

This post received KUDOS

meprarth wrote:

Please tell me what is wrong with my approach1/p > r/(r^2+2) r^2+2-pr>0 when p=rr^2-(r*r)+2=2 which is >0

You can't cross multiply "-ve" numbers. We don't know what's "p", a "-ve" or "+ve"

If p=-ve, then cross multiplying will reverse the inequality sign.

\frac{1}{-2}>\frac{-2}{1} Cross multiply:

1>4 , which is WRONG.

Thus,

1/p > r/(r^2+2) cannot be written as

r^2+2-pr>0 as the signs for p and r are unknown.

You can cross multiply a "+ve" number because that doesn't hurt the inequality.

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

SVP

Joined: 16 Nov 2010

Posts: 1691

Location: United States (IN)

Concentration: Strategy, Technology

Followers: 30

Kudos [? ]:
285
[0 ] , given: 36

Re: Is 1/p > r/(r^2 +2) [#permalink ]
17 Apr 2011, 18:15

The question asks :

1/p - r/(r^2 + 2) > 0

(1) says p = r, so

1/r - r/(r^2 + 2) > 0

(r^2 + 2 - r^2)/r(r^2 + 2) > 0

or, 2/r(r^2 + 2) > 0

r^2 + 2 is positive, but the sign r is not known, so (1) is insufficient.

(2) says r > 0

but we still don't know for sure, e.g.,

p = 1, r = 1

r^2 + 2 = 3

1/p > 1/3

p = 10, r = 3

1/10 < 1/3

So (2) is insufficient

(1) and (2) says 2/r(r^2 + 2) > 0 and r > 0

So sufficient

Answer - C

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager

Status: ==GMAT Ninja==

Joined: 08 Jan 2011

Posts: 247

Schools: ISB, IIMA ,SP Jain , XLRI

WE 1: Aditya Birla Group (sales)

WE 2: Saint Gobain Group (sales)

Followers: 4

Kudos [? ]:
43
[0 ] , given: 46

Re: Is 1/p > r/(r^2 +2) [#permalink ]
18 Apr 2011, 11:58

fluke wrote:

junior wrote:

Is 1/p > r/(r^2 + 2)? 1. p = r 2. r > 0

Is

\frac{1}{p} > \frac{r}{r^2+2} ?

1. p=r

\frac{1}{r} > \frac{r}{r^2+2} \frac{r^2+2}{r} > r r+\frac{2}{r} > r Is

\frac{2}{r} > 0 We don't know sign of r.

Not Sufficient.

2. r > 0

We don't know anything about p.

Not Sufficient.

Combining both;

We know

\frac{2}{r} > 0 as

r>0 Sufficient.

Ans: "C"

Dear Fluke

as far as i know inequilities

you cant cross multiply untill the signs are positive

you yourself said following first statement that we dont know the signs

and you even cross multiplied

rather it should have been

\frac{2}{r(r^2+2)} > 0 not 2/r

please correct me if i am wrong

_________________

WarLocK _____________________________________________________________________________ The War is oNNNNNNNNNNNNN for 720+ see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html do not hesitate me giving kudos if you like my post.

Math Forum Moderator

Joined: 20 Dec 2010

Posts: 2048

Followers: 128

Kudos [? ]:
899
[0 ] , given: 376

Re: Is 1/p > r/(r^2 +2) [#permalink ]
18 Apr 2011, 12:06

Warlock007 wrote:

fluke wrote:

junior wrote:

Is 1/p > r/(r^2 + 2)? 1. p = r 2. r > 0

Is

\frac{1}{p} > \frac{r}{r^2+2} ?

1. p=r

\frac{1}{r} > \frac{r}{r^2+2} \frac{r^2+2}{r} > r r+\frac{2}{r} > r Is

\frac{2}{r} > 0 We don't know sign of r.

Not Sufficient.

2. r > 0

We don't know anything about p.

Not Sufficient.

Combining both;

We know

\frac{2}{r} > 0 as

r>0 Sufficient.

Ans: "C"

Dear Fluke

as far as i know inequilities

you cant cross multiply untill the signs are positive

you yourself said following first statement that we dont know the signs

and you even cross multiplied

rather it should have been

\frac{2}{r(r^2+2)} > 0 not 2/r

please correct me if i am wrong

r^2+2 \ge 2 , which is +ve. Thus, I multiplied.

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

Director

Joined: 01 Feb 2011

Posts: 770

Followers: 14

Kudos [? ]:
81
[0 ] , given: 42

Re: Is 1/p > r/(r^2 +2) [#permalink ]
22 Apr 2011, 18:09

1. Not sufficient. we need to find out the following is true or not 1/r > r/(r^2+2)? => 2/(r* (r^2+2)) >0 ? => r*(r^2+2)>0 ? => r >0 , (r^2+2)>0 (case 1 ) or r <0 , (r^2+2)<0 (case 2) case 2 cant be true as r^2 cannot be negative. => r>0? 2. Not sufficient as we dont know anything about p. together we know p=r and r>0. Sufficient. Answer is C.

Senior Manager

Joined: 24 Mar 2011

Posts: 469

Location: Texas

Followers: 4

Kudos [? ]:
54
[0 ] , given: 20

Is 1/p > r/(r^2 + 2)? (1) p = r (2) r>0

Math Forum Moderator

Joined: 20 Dec 2010

Posts: 2048

Followers: 128

Kudos [? ]:
899
[0 ] , given: 376

Re: DS - Inequalities [#permalink ]
04 May 2011, 08:59

agdimple333 wrote:

Is 1/p > r/(r^2 + 2)? (1) p = r (2) r>0

Sol:

Is \hspace{3} \frac{1}{p} > \frac{r}{(r^2 + 2)}? 1.

p=r \frac{1}{r} > \frac{r}{(r^2 + 2)} \frac{1}{r} - \frac{r}{(r^2 + 2)}>0 \frac{r^2+2-r^2}{r(r^2+2)}>0 \frac{2}{r(r^2+2)}>0 \frac{2}{r}>0 -------------------------1 But, we don't know anything about r's sign.

Not Sufficient.

2.

r>0 ------------------------2 p=0.000000000000000000000001 and r=1; answer will be YES.

p=-1 and r=1; answer will be NO.

Not Sufficient.

Combined, using eq1 and eq2:

\frac{2}{r}>0 as

r>0 Sufficient.

Ans: "C"

P.S.: I remember answering this before. I am just not able to locate that thread.

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

Intern

Status: ThinkTank

Joined: 07 Mar 2009

Posts: 28

Followers: 0

Kudos [? ]:
6
[0 ] , given: 3

Re: DS - Inequalities [#permalink ]
04 May 2011, 09:04

The concept tested here is inequalities

I dont see a rephrasing here because it depends on the sign of p. We can not cross multiply.

1) r > 0 but we have no info on p so Insuff - AD out

2) p =r so the question is 1/r > r/ r^2 +2 ?. If we plug r = 1 we get yes answer. However, if we plug -2 we get no. Insuff - B out

1+2) we can infer p^2 +2 > p^2 ? => 2 > 0? always yes for any p. Suff

The answer is C

_________________

http://www.hannibalprep.com

Senior Manager

Joined: 24 Mar 2011

Posts: 469

Location: Texas

Followers: 4

Kudos [? ]:
54
[0 ] , given: 20

Fig wrote:

(C) for me

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

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

From 1 p=r

So,

1/p - r/(r^2+2)

= 1/r - r/(r^2+2)

= [(r^2+2) - r^2] / [r*(r^2+2)]

= 2 / [r*(r^2+2)]

= 1/r * 2/(r^2+2)

As, r^2 >=0, we know that r^2 + 2>= 2 > 0

So, 1/p - r/(r^2+2) > 0 if and only if r > 0. But we do not know if r > 0.

INSUFF.

From 2 r > 0 and nothing about p.

INSUFF.

Both 1 & 2 We have the condition r > 0 for the statment 1 to be concluded.

SUFF.

thank you. I like your explanation.

VP

Status: There is always something new !!

Affiliations: PMI,QAI Global,eXampleCG

Joined: 08 May 2009

Posts: 1365

Followers: 11

Kudos [? ]:
135
[0 ] , given: 10

Re: Is 1/p > r/(r^2 +2) [#permalink ]
04 May 2011, 22:22

a p=r= positive LHS > RHS

p=r= negative LHS <RHS not sufficient.

b p<0 r>0 and p,r>0 give different values. not sufficient.

a+b p,r>0 hence LHS > RHS. hence C

_________________

Visit -- http://www.sustainable-sphere.com/ Promote Green Business,Sustainable Living and Green Earth !!

Re: Is 1/p > r/(r^2 +2)
[#permalink ]
04 May 2011, 22:22