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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Equation

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 436
Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members
Thanked: 72 times

by manpsingh87 » Mon Feb 28, 2011 1:52 am
yellowho wrote:What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


OA is E. What?
1) can be written as x^2+y^2-2xy=1;

(x-y)^2=1; from here two different cases are possible;------------a)
x-y=1; x-y= -1;

2) x^2+y^2+2xy= 4;
(x+y)^2 = 2^2; similarly as a) we have;

x+y=2; x+y=-2;

By using 1 and 2 alone we cannot find the value of x^2+y^2 by combining 1 and 2 also we will have different possible combination and hence different values.

Hence the value x^2+y^2 cannot be found uniquely by using given conditions.

i hope it helps..!!!
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

by sanju09 » Mon Feb 28, 2011 2:00 am
yellowho wrote:What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


OA is E. What?

(1) If x^2 + y^2 = 2 x y + 1 then (x - y) ^2 = 1 or x - y = ±1, which cannot give us the value of x^2 + y^2. Insufficient

(2) If x^2 + y^2 = 4 - 2 x y then (x + y) ^2 = 4 or x + y = ±2, which cannot give us the value of x^2 + y^2. Insufficient

Taken together, we have different systems of linear equations in two variables, so [spoiler]no exclusive x and/or y could be determined that could answer x^2 + y^2 exclusively.

E[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 233
Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members
Location: New York
Thanked: 7 times

by yellowho » Mon Feb 28, 2011 2:01 am
(1) x^2 + y^2 = 2xy + 1 => x^2+y^2-1= 2xy
(2) x^2 + y^2 = 4 - 2xy => x^2+y^2-4=-2xy=> -x^2-y^2+4=2xy

Set them equal:

x^2+y^2-1=-x^2-y^2+4

2(X^2+y^2)=5

x^2+y^2=5/2

Since it deals with quadratic there could be other solutions? is that why its e?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 233
Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members
Location: New York
Thanked: 7 times

by yellowho » Mon Feb 28, 2011 2:03 am
Sanju,

Can you explain this a little more:

"Taken together, we have different systems of linear equations in two variables, so [spoiler][b]no exclusive x and/or y could be determined that could answer x^2 + y^2 exclusively."

I'm not familiar with math language.


[quote="sanju09"][quote="yellowho"]What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


OA is E. What?[/quote]


(1) If x^2 + y^2 = 2 x y + 1 then (x - y) ^2 = 1 or x - y = ±1, which cannot give us the value of x^2 + y^2. Insufficient

(2) If x^2 + y^2 = 4 - 2 x y then (x + y) ^2 = 4 or x + y = ±2, which cannot give us the value of x^2 + y^2. Insufficient

Taken together, we have different systems of linear equations in two variables, so [spoiler][b]no exclusive x and/or y could be determined that could answer x^2 + y^2 exclusively.

E[/b][/spoiler][/quote]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Feb 28, 2011 2:22 am
yellowho wrote:What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


OA is E. What?
The OA is incorrect.

Combining the 2 statements:
x-y = ±1.
x+y = ±2.

Solving for x-y = 1 and x+y = 2, we get x=3/2, y=1/2.
Solving for x-y = 1 and x+y = -2, we get x=-1/2, y=-3/2.
Solving for x-y = -1 and x+y = 2, we get x=1/2, y=3/2.
Solving for x-y = -1 and x+y = -2, we get x=-3/2, =-1/2.

In each case, x²+y² = 10/4 = 5/2.
Sufficient.

Alternatively, we could solve as yellowho correctly did above.

The correct answer is C.
Last edited by GMATGuruNY on Mon Feb 28, 2011 2:26 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

by sanju09 » Mon Feb 28, 2011 2:24 am
yellowho wrote:Sanju,

Can you explain this a little more:

"Taken together, we have different systems of linear equations in two variables, so [spoiler]no exclusive x and/or y could be determined that could answer x^2 + y^2 exclusively."

I'm not familiar with math language.


I have worked these out separately and got the same answer for x^2 + y^2.


[spoiler]C[/spoiler]
Last edited by sanju09 on Mon Feb 28, 2011 2:31 am, edited 1 time in total.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 233
Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members
Location: New York
Thanked: 7 times

by yellowho » Mon Feb 28, 2011 2:28 am
GMATGuruNY,

Is my method correct? With quadratic, I'm always afraid of weird things that makes regular algebra illegal.
Or is your method the only way we know for sure?
[quote="GMATGuruNY"][quote="yellowho"]What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


OA is E. What?[/quote]

The OA is incorrect.

Combining the 2 statements:
x-y = ±1.
x+y = ±2.

Solving for x-y = 1 and x+y = 2, we get x=3/2, y=1/2.
Solving for x-y = 1 and x+y = -2, we get x=-1/2, y=-3/2.
Solving for x-y = -1 and x+y = 2, we get x=1/2, y=3/2.
Solving for x-y = -1 and x+y = -2, we get x=-3/2, =-1/2.

In each case, x²+y² = 10/4 = 5/2.
Sufficient.

Alternatively, we could solve as yellowho correctly did above.

The correct answer is [spoiler]C[/spoiler].[/quote]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Feb 28, 2011 2:33 am
yellowho wrote:GMATGuruNY,

Is my method correct? With quadratic, I'm always afraid of weird things that makes regular algebra illegal.
Or is your method the only way we know for sure?
GMATGuruNY wrote:
yellowho wrote:What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


OA is E. What?
The OA is incorrect.

Combining the 2 statements:
x-y = ±1.
x+y = ±2.

Solving for x-y = 1 and x+y = 2, we get x=3/2, y=1/2.
Solving for x-y = 1 and x+y = -2, we get x=-1/2, y=-3/2.
Solving for x-y = -1 and x+y = 2, we get x=1/2, y=3/2.
Solving for x-y = -1 and x+y = -2, we get x=-3/2, =-1/2.

In each case, x²+y² = 10/4 = 5/2.
Sufficient.

Alternatively, we could solve as yellowho correctly did above.

The correct answer is C.
Your methodology is fine. We can always add two equations together, whether the equations are linear or quadratic.

If the question had asked for the values of x and y individually, the correct answer would be E. But since the question asks only for the value of x²+y², the correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members
Thanked: 47 times
GMAT Score:640

by HSPA » Mon Feb 28, 2011 10:09 pm
What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


IMO C
Using both....
Here 2xy+1 = 4-2xy => 2xy = 1.5
So I got x^2+y^2 = 1.5+1 or (4-1.5)

Ans: 2.5
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

by sanju09 » Mon Feb 28, 2011 10:59 pm
HSPA wrote:What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy


IMO C
Using both....
Here 2xy+1 = 4-2xy => 2xy = 1.5
So I got x^2+y^2 = 1.5+1 or (4-1.5)

Ans: 2.5
superb
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1