• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Q from GMAT Prep

This topic has 1 expert reply and 3 member replies

Q from GMAT Prep

Post
Is 1/p > r/(r*r + 2) ?

a. p = r
b. r > 0

Answer - C : a and b together sufficient; why not A - only a sufficient?

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member Default Avatar
Joined
17 May 2011
Posted:
1448 messages
Followed by:
53 members
Upvotes:
375
Post
Hi,
From(1): p=r
Consider 1/p - r/(r^2 + 2) = 1/r - r/(r^2 + 2) = [(r*r+2) - r*r]/r*(r^2 + 2) = 2/r(r^2+2)
r^2+2 is always positive
So, sign of 2/r(r^2 + 2) depends on sign of r.
If r is positive it will be positive, if r is negative, it will be negative
Not sufficient
From(2): r>0
No info. about p
Not sufficient
Both (1)&(2):
1/p - r/(r^2 + 2) = 2/r(r^2+2)
As r>0, 2/r(r^2+2) > 0
So, 1/p - r/(r^2 + 2) > 0
Sufficient

Hence, C

_________________
Cheers!

Things are not what they appear to be... nor are they otherwise

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Mumbai wrote:
Is 1/p > r/(r^2 + 2) ?
a. p = r
b. r > 0
Answer C
Statement 1:
If we replace p with r, the target question becomes "Is 1/r > r/(r^2 + 2)?"
In this form, it might be tough to answer the new target question.
However, since (r^2 + 2) must be positive, we can multiply both sides of the target question by (r^2 + 2) to get a new target question: Is (r^2 + 2)/r > r?
From here, we can simplify the left-hand-side to get Is r + 2/r > r?
Finally, if we subtract r from both sides of the target question, we get Is 2/r > 0?
At this point, it's easy to answer the target question.
2/r can be greater than zero or it can be less than zero.
As such, statement 1 is not sufficient.

Statement 2:
Since we are given no information about p, statement 2 is not sufficient.

Statements 1 AND 2:
Statement 1 allowed us to rewrite the question as Is 2/r > 0?
Since statement 2 tells us that r is positive, we can now answer the new target question with certainty (2/r is definitely greater than zero).

So, the answer is C

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
Brent@GMATPrepNow wrote:
Mumbai wrote:
Is 1/p > r/(r^2 + 2) ?
a. p = r
b. r > 0
Answer C
Statement 1:
If we replace p with r, the target question becomes "Is 1/r > r/(r^2 + 2)?"
In this form, it might be tough to answer the new target question.
However, since (r^2 + 2) must be positive, we can multiply both sides of the target question by (r^2 + 2) to get a new target question: Is (r^2 + 2)/r > r?
From here, we can simplify the left-hand-side to get Is r + 2/r > r?
Finally, if we subtract r from both sides of the target question, we get Is 2/r > 0?
At this point, it's easy to answer the target question.
2/r can be greater than zero or it can be less than zero.
As such, statement 1 is not sufficient.

Statement 2:
Since we are given no information about p, statement 2 is not sufficient.

Statements 1 AND 2:
Statement 1 allowed us to rewrite the question as Is 2/r > 0?
Since statement 2 tells us that r is positive, we can now answer the new target question with certainty (2/r is definitely greater than zero).

So, the answer is C
Hi Brent,

I'am getting the ans as A...don't know where I'm going wrong..

(r^2+2)/p > r

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

Ques rephrased...

Is r^2+2-rp > 0 (Is this step wrong)
Now, if r=p then,

r^2 + 2 - r^2 >0
i.e 2>0 (Sufficient)

Plz help me to find where I'm going wrong

  • +1 Upvote Post
  • Quote
  • Flag
Master | Next Rank: 500 Posts
Joined
23 Jan 2009
Posted:
131 messages
Followed by:
15 members
Upvotes:
59
Post
You can't multiply both sides of an inequality by a variable (p here) unless you know it is positive or negative.

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

Ques rephrased...

Is r^2+2-rp > 0 (Is this step wrong? Yes)

Here is a video explanation:
http://www.gmatquantum.com/shared-posts1/2011/7/18/gmatprep-inequality-15.html

Dabral

_________________
Free Video Explanations: 2018 OFFICIAL GUIDE FOR GMAT REVIEW.

  • +1 Upvote Post
  • Quote
  • Flag
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 32 first replies
5 GMATGuruNY 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

159 posts
2 image description Max@Math Revolution

Math Revolution

92 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

60 posts
4 image description Ian Stewart

GMATiX Teacher

50 posts
5 image description GMATGuruNY

The Princeton Review Teacher

37 posts
See More Top Beat The GMAT Experts