• 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

Inequality

This topic has 1 expert reply and 1 member reply

Inequality

Post
If 'a' not equal to 0, is 1/a> a/(b^4+3)?

1. a^2=b^2
2. a^2=b^4

Please help.

_________________
Thanks,
Bharat.

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member
Joined
14 Aug 2012
Posted:
1556 messages
Followed by:
34 members
Upvotes:
448
Target GMAT Score:
750
GMAT Score:
650
Post
pareekbharat86 wrote:
If 'a' not equal to 0, is 1/a> a/(b^4+3)?

1. a^2=b^2
2. a^2=b^4

Please help.
To find: 1/a > a/(b^4 + 3)

Statement 1:
a^2=b^2
==> either a = b or a = -b
If a = b, then
1/b > b/(b^4 + 3)
b^4 + 3 > b^2

If a = -b
1/-b > -b/(b^4+3)
b/(b^4 + 3) > 1/b
b^2 > b^4 + 3
INSUFFICIENT

Statement 2:
a = b^2 or -a = b^2
if a = b^2
1/a > a/(b^4 + 3)
1/b^2 > b^2/(b^4 + 3)
b^4 + 3 > b^4
3 > 0
YES

if -a = b^2
-a/(b^4+3) > 1/-a
b^2/(b^4+3) > 1/b^2
b^4 > b^4 + 3
0 > 3
NO

Combining...
a = b or a = -b
a = b^2 or -a = b^2
We cannot deduce anything

{E}????

_________________
R A H U L

  • +1 Upvote Post
  • Quote
  • Flag
Post
Quote:
If 'a' not equal to 0, is 1/a> a/(b^4+3)?

1. a^2=b^2
2. a^2=b^4
There is no obvious way to rephrase this question. We don't want to cross-multiply, since we don't know whether a or b^4 + 3 is negative. So, all we can do is consider the statements.

1) As Rahul said, we want to translate this question as a=b or a=-b. In other words, |a|=|b|.
We can quickly test numbers to prove insufficiency:

If a=2 and b=2, then:
(1/2) > 2/(16 + 3)
yes

If a=-2 and b=2, then:
(1/-2) > -2/(16 + 3)
no
Insufficient

2) If a^2=b^4, then |a|=b^2
Again, test values:

If a=4 and b=2, then:
1/4 > 4/(16 + 3)
yes

If a=-4 and b=2, then:
1/-4 > -4/(16 + 3)
no
Insufficient

1&2) Together, the statements tell us something very significant. The statements both have to be true, and thus can't contradict each other. If a^2=b^2 and a^2=b^4, then a^2 has to be equal to 1 or 0. The question stem tells us that a can't be 0, so a^2 has to be 1.

Thus, a=1 or a=-1, and b=1 or b=-1. Test values again:

If a=1 and b=1, then:
1/1 > 1/(1 +3)
yes

If a=-1 and b=1, then:
1/-1 > -1/(1 + 3)
no
Insufficient

The answer is E.[/i]

_________________


Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
  • 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas 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

Top First Responders*

1 Jay@ManhattanReview 71 first replies
2 Brent@GMATPrepNow 67 first replies
3 GMATGuruNY 43 first replies
4 Ian Stewart 27 first replies
5 Scott@TargetTestPrep 18 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

221 posts
2 image description Max@Math Revolution

Math Revolution

93 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

90 posts
4 image description Jay@ManhattanReview

Manhattan Review

73 posts
5 image description GMATGuruNY

The Princeton Review Teacher

66 posts
See More Top Beat The GMAT Experts