It is currently 21 Feb 2018, 13:04

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior SC Moderator
User avatar
D
Joined: 14 Nov 2016
Posts: 1277
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2 [#permalink]

Show Tags

New post 16 Mar 2017, 00:30
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

29% (00:58) correct 71% (01:26) wrong based on 58 sessions

HideShow timer Statistics

Is \(x^3+y^3>x^2 +y^2\)?

(1) \(x+y > x^2+y^2\)
(2) \(x^4 + y^4 > x^2+y^2\)
[Reveal] Spoiler: OA

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

SC Moderator
User avatar
P
Joined: 13 Apr 2015
Posts: 1583
Location: India
Concentration: Strategy, General Management
WE: Analyst (Retail)
GMAT ToolKit User Premium Member CAT Tests
Re: Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2 [#permalink]

Show Tags

New post 16 Mar 2017, 04:02
Is x^3 + y^3 > x^2 + y^2 ?
x^3 - x^2 + y^3 - y^2 > 0?
x^2(x - 1) + y^2(y - 1) > 0?

St1: x + y > x^2 + y^2
x^2 - x + y^2 - y < 0
x(x - 1) + y(y - 1) < 0 --> Possible when x is between 0 and 1 and y is between 0 and 1.
Hence x^2(x - 1) + y^2(y - 1) is not greater than 0.
Sufficient.

St2: x^4 - x^2 +y^4 - y^2 > 0
x^2(x^2 - 1) + y^2(y^2 - 1) > 0 --> x and y can be -ve or +ve
If x < -1 and y < -1 then x^3 + y^3 cannot be greater than x^2 + y^2
If x > 1 and y > 1 then x^3 + y^3 > x^2 + y^2.
Not Sufficient.

I think the answer has to be A and not E. Let me know if I have made an error.
Intern
Intern
avatar
Joined: 17 Mar 2017
Posts: 1
Re: Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2 [#permalink]

Show Tags

New post 17 Mar 2017, 09:14
Vyshak wrote:
Is x^3 + y^3 > x^2 + y^2 ?
x^3 - x^2 + y^3 - y^2 > 0?
x^2(x - 1) + y^2(y - 1) > 0?

St1: x + y > x^2 + y^2
x^2 - x + y^2 - y < 0
x(x - 1) + y(y - 1) < 0 --> Possible when x is between 0 and 1 and y is between 0 and 1.

x(x - 1) + y(y - 1) < 0 does not require that both x and y be between 0 and 1.
If x=0.2 and y=1.1, then x(x - 1) + y(y - 1) = (0.2)(-0.8) + (1.1)(0.1) = -0.16 + 0.11 = -0.05.

Quote:
Hence x^2(x - 1) + y^2(y - 1) is not greater than 0.

If x=0.2 and y=1.1. then x²(x - 1) + y²(y - 1) = (0.04)(-0.8) + (1.21)(0.1) = -0.032 + 0.121 = 0.089, which is greater than 0.

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 17 Apr 2016
Posts: 102
Re: Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2 [#permalink]

Show Tags

New post 17 Mar 2017, 18:45
ziyuen wrote:
Is \(x^3+y^3>x^2 +y^2\)?

(1) \(x+y > x^2+y^2\)
(2) \(x^4 + y^4 > x^2+y^2\)


The first statement implies 0<x<1 and 0<y<1.

And second implies x>0 and y>0.

So IMO answer should be D.

Where am I going wrong here? :?
Manager
Manager
User avatar
S
Joined: 23 Dec 2016
Posts: 65
Schools: Fuqua
GMAT 1: 720 Q49 V40
GPA: 3.33
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2 [#permalink]

Show Tags

New post 18 Mar 2017, 07:03
1
This post was
BOOKMARKED
Statement 1 is not sufficient because there can be two scenarios.

1. 0<X<1 and 0<Y<1. in this case x^3 + y^3 > x^2 + y^2 is not true

2. Either X or Y is between (0;1) and the other is slightly bigger than 1.
For example X=1.045 and Y=0.95
X+Y=1.995, X^2+Y^2=1.994525 and X^3+Y^3=1.998
_________________

If you find my solution useful, hit the "Kudos" button

Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2   [#permalink] 18 Mar 2017, 07:03
Display posts from previous: Sort by

Is x^3+y^3>x^2 +y^2? (1)x+y>x^2+y^2 (2) x^4 + y^4 > x^2 + y^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.