• 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

Is x > 0 ?

This topic has 2 expert replies and 0 member replies

Is x > 0 ?

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Is x > 0 ?

(1) x < x^2
(2) x < x^3

The OA is the option E.

Why is not sufficient any of the statements? Could anyone explain to me how to prove this? I'd be thankful for your help.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
Hi VJesus12,

We're asked if X is greater than 0. This is a YES/NO question and can be approached in a couple of different ways, including by using Number Properties.

1) X < X^2

For X^2 to be greater than X, there are 2 possibilities:
1) X is ANY negative number... at which point the answer to the question is NO.
2) X is a positive number GREATER than 1... at which point the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) X < X^3

For X^3 to be greater than X, there are 2 possibilities:
1) X is a negative fraction... at which point the answer to the question is NO.
2) X is a positive number GREATER than 1... at which point the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we have some examples that 'fit' BOTH Facts:
1) X is a negative fraction... at which point the answer to the question is NO.
2) X is a positive number GREATER than 1... at which point the answer to the question is YES.
Combined, INSUFFICIENT

Final Answer:E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
VJesus12 wrote:
Is x > 0 ?

(1) x < x²
(2) x < x³
Target question: Is x > 0 ?
Let's go straight to...

Statements 1 and 2 combined
Statement 1 tells us that x < x²
Statement 2 tells us that x < x³
There are several values of x that satisfy BOTH statements. Here are two:
Case a: x = 2. Notice that 2 < 2² AND 2 < 2³. In this case, the answer to the target question is YES, x IS greater than 0
Case b: x = -1/2. Notice that (-1/2) < (-1/2)² AND (-1/2) < (-1/2)³. In this case, the answer to the target question is NO, x is NOT greater than 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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

Sign up for our free Question of the Day emails
And check out all of our 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!
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • 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
  • 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
  • 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 GMATGuruNY 58 first replies
2 Brent@GMATPrepNow 44 first replies
3 Jay@ManhattanReview 41 first replies
4 Ian Stewart 29 first replies
5 ceilidh.erickson 17 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

212 posts
2 image description fskilnik@GMATH

GMATH Teacher

128 posts
3 image description Max@Math Revolution

Math Revolution

87 posts
4 image description GMATGuruNY

The Princeton Review Teacher

85 posts
5 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

68 posts
See More Top Beat The GMAT Experts