Find all School-related info fast with the new School-Specific MBA Forum

It is currently 13 Jul 2014, 18:45

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x and y are positive, is x^3 > y?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 144
Followers: 3

Kudos [?]: 48 [0], given: 12

GMAT Tests User Reviews Badge
If x and y are positive, is x^3 > y? [#permalink] New post 23 Jun 2010, 11:30
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

48% (02:55) correct 52% (00:28) wrong based on 25 sessions
If x and y are positive, is x^3 > y?

(1) \sqrt{x} > y
(2) x > y

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-is-x-3-y-100086.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jun 2014, 01:22, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Manager
Manager
avatar
Joined: 03 May 2010
Posts: 89
WE 1: 2 yrs - Oilfield Service
Followers: 11

Kudos [?]: 57 [0], given: 7

GMAT Tests User Reviews Badge
Re: If x and y are positive, is x^3 > y? [#permalink] New post 23 Jun 2010, 23:29
Statement 1 is actually "root(x) > y"

x>0 and y>0 Is x^3 > y?

From statement 1:
root(x) > y
Test cases:
x = 4 and y = 1 => root(x) = 2 > 1. x^3 = 64 > 1 ... Answer : Yes
x = 0.01 and y = 0.005 => root(x) = 0.1 > 0.05. x^3 = 0.001 < 0.005 ...Answer: No
INSUFFICIENT

From statement 2:
x > y
Test cases:
x = 2 and y = 3 => x^3 = 8 > 3. Answer -Yes
x = 0.1 and y = 0.01 => x^3 = 0.001 < 0.01. Answer - No
INSUFFICIENT

Both 1 and 2 together:
Test cases:
x = 4 and y = 1 satisfies both statements, and x^3 > y is true.
x = 0.01 and y = 0.005 satisfies both statements and x^3>y is false.
INSUFFICIENT.

Pick E.
Manager
Manager
avatar
Joined: 17 Jul 2013
Posts: 92
Followers: 0

Kudos [?]: 1 [0], given: 52

Re: If x and y are positive, is x^3 > y? [#permalink] New post 26 Jun 2014, 23:36
Hi Bunuel,

Can we do this ques based on graphs .. I am working on a technique that could help me to hit all in equality questions.

Please suggest ...

Thanks
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18523
Followers: 3197

Kudos [?]: 21437 [0], given: 2547

Re: If x and y are positive, is x^3 > y? [#permalink] New post 27 Jun 2014, 01:27
Expert's post
GmatDestroyer2013 wrote:
Hi Bunuel,

Can we do this ques based on graphs .. I am working on a technique that could help me to hit all in equality questions.

Please suggest ...

Thanks


I wouldn't suggest to use graph approach for this question because x^3 and \sqrt{x} functions are not easy to plot and compare. Below are two approaches which are good for it.

If x and y are positive, is x^3>y?

NUMBER PLUGGING:

(1) \sqrt{x}>y --> if x=1 and y=\frac{1}{2} then the answer will be YES but if x=\frac{1}{4} and y=\frac{1}{5} then the answer will be NO. Two different answers, hence not sufficient.

(2) x>y --> if x=1 and y=\frac{1}{2} then the answer will be YES but if x=\frac{1}{4} and y=\frac{1}{5} then the answer will be NO. Two different answers, hence not sufficient.

(1)+(2) Both examples are valid for combined statements, so we still have two answers. Not sufficient.

Answer: E.

ALGEBRAIC APPROACH:

For 1\leq{x}: ------\sqrt{x}----x----x^3, so 1\leq{\sqrt{x}}\leq{x}\leq{x^3} (the case \sqrt{x}=x=x^3 is when x=1). y is somewhere in green zone (as y<\sqrt{x} and y<x), so if we have this case answer is always YES: y<x^3.

But:

For 0<x<1: 0----x^3----x----\sqrt{x}----1, so 0<x^3<x<\sqrt{x}. y is somewhere in green or red zone (as y<\sqrt{x} and y<x), so if we have this case answer is sometimes YES: y<x^3 (if y is in green zone), and sometimes NO: x^3<y (if y is in red zone). In fact in this case y=x^3 is also possible, for example when x=\frac{1}{2} and y=\frac{1}{8}

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-is-x-3-y-100086.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If x and y are positive, is x^3 > y?   [#permalink] 27 Jun 2014, 01:27
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic If x and y are positive, is x^3 > y? udaymathapati 7 30 Aug 2010, 08:38
1 Is x^3 > y hrish88 2 14 Nov 2009, 04:15
4 Experts publish their posts in the topic If x and y are positive, is x^3 > y? Wengen 15 24 Jul 2009, 08:54
1 If x and y are positive, is x^3 > y? hbs2012 4 24 Dec 2008, 14:04
If x and y are positive, is x^3 > y? (1) square root Antmavel 6 16 Oct 2004, 05:59
Display posts from previous: Sort by

If x and y are positive, is x^3 > y?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.