• NEW! FREE Beat The GMAT Quizzes  Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 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 PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Q from GMAT Prep tagged by: Brent@GMATPrepNow ##### This topic has 1 expert reply and 3 member replies 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? Legendary Member Joined 17 May 2011 Posted: 1448 messages Followed by: 53 members Upvotes: 375 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 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13035 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 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 Sign up for free Question of the Day emails And check out all of these free resources 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! Newbie | Next Rank: 10 Posts Joined 09 Jan 2011 Posted: 5 messages 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 Master | Next Rank: 500 Posts Joined 23 Jan 2009 Posted: 131 messages Followed by: 15 members Upvotes: 59 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. • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### 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 Scott@TargetTestPrep

Target Test Prep

159 posts
2 Max@Math Revolution

Math Revolution

92 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

60 posts
4 Ian Stewart

GMATiX Teacher

50 posts
5 GMATGuruNY

The Princeton Review Teacher

37 posts
See More Top Beat The GMAT Experts