BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is x2 + y2 > 6

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 216
Joined: Wed Jul 23, 2008 2:35 am
Location: Pune, India
Thanked: 5 times
GMAT Score:700

by ayushiiitm » Fri Jun 25, 2010 5:46 pm
stem 1 says (x+y)^2>6

i.e x^2+y^2+2xy>6

you may be tempted here to conclude that then (x+y)^2<6

think of the case now like this
x^2+y^2+2xy>6

then may be x^2+y^2 was equal to 4 and 2xy was equal to 3 so x^2+y^2 <6, even though x^2+y^2+2xy>6
or may be x^2+y^2 was equal to 8 and 2xy was equal to 1 so x^2+y^2 >6 even though x^2+y^2+2xy>6

insufficient

stem 2 is not sufficient as we see


using both stem 1 and 2

x^2+y^2+2xy>6....putting value of xy
x^2+y^2>4

so x^2+y^2 could be equal to 5

or x^2+y^2 could be equal to 10

so insufficient
Success is a journey.....enjoy every moment of it
Top
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Thu Mar 25, 2010 3:35 am
Thanked: 1 times

by naki009 » Fri Jun 25, 2010 7:34 pm
ayushiiitm wrote:stem 1 says (x+y)^2>6

i.e x^2+y^2+2xy>6

you may be tempted here to conclude that then (x+y)^2<6

think of the case now like this
x^2+y^2+2xy>6

then may be x^2+y^2 was equal to 4 and 2xy was equal to 3 so x^2+y^2 <6, even though x^2+y^2+2xy>6
or may be x^2+y^2 was equal to 8 and 2xy was equal to 1 so x^2+y^2 >6 even though x^2+y^2+2xy>6

insufficient

stem 2 is not sufficient as we see


using both stem 1 and 2

x^2+y^2+2xy>6....putting value of xy
x^2+y^2>4

so x^2+y^2 could be equal to 5

or x^2+y^2 could be equal to 10

so insufficient
Thank you.. thats a really nice explanation
Top
Master | Next Rank: 500 Posts
Posts: 151
Joined: Thu Apr 22, 2010 4:07 pm
Thanked: 14 times

by Haaress » Sat Jun 26, 2010 2:52 pm
Good question. Thanks for posting it.
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Wed Dec 16, 2009 1:48 pm

by swiftwolff » Sat Feb 04, 2012 7:12 pm
I find (2)xy=2 sufficient somehow... because there are only limited possibilities for the product of x and y, It could be x=2 y=1, x=1 y=2, x=-2 y=-1, x=-1 y=-2, x=square root of 2 y=square root of 2 (also negative square root of 2). When square all of the set, all of the answer sets will add up to be less than 6. Can anyone comment on this?
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Wed Dec 16, 2009 1:48 pm

by swiftwolff » Sat Feb 04, 2012 7:14 pm
Never mind, x could be 6 and y could be 1/3.... dumb me... sorry
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Feb 04, 2012 8:47 pm
naki009 wrote:Is x^2 + y^2 > 6?
(1) (x + y)^2 > 6
(2) xy = 2

OA : E

I can anyone please explain the answer for this ?
(1) (x + y)² > 6 implies x² + y² + 2xy > 6
If x² + y² = 5 and 2xy = 3, then x² + y² < 6
If x² + y² = 10 and 2xy = 3, then x² + y² > 6
No definite answer; NOT sufficient.

(2) xy = 2
If x = y = √2, then x² + y² = 4 < 6
If x = 10, y = 1/5, then x² + y² = 100 + 1/25 > 6
No definite answer; NOT sufficient.

Combining (1) and (2), x² + y² + 2xy > 6
x² + y² + 2(2) > 6
x² + y² + 4 > 6
x² + y² > 2
If x² + y² = 5, then x² + y² < 6
If x² + y² = 10 , then x² + y² > 6
No definite answer; NOT sufficient.

The correct answer is E.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Post new topic Post Reply
• Page 1 of 1