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

It is currently 25 Sep 2016, 00:24
GMAT Club Tests

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

What is the value of x^2 + y^2 ?

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

Hide Tags

Intern
Intern
avatar
Joined: 26 Apr 2012
Posts: 34
Followers: 1

Kudos [?]: 8 [0], given: 27

GMAT ToolKit User
What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 23 Nov 2012, 07:29
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

57% (02:08) correct 43% (01:10) wrong based on 137 sessions

HideShow timer Statistics

What is the value of x^2 + y^2 ?

(1) x^2 + y^2 = 2xy+1
(2) x^2 + y^2 = 4 - 2xy

I have an official answer but I was thinking that it is wrong.
This is a question from GMATHacks Algebra Challange set.


OA SOLUTION

[Reveal] Spoiler:
77. E
Explanation: This question rigorously tests your familiarity with common
binomials. The only way to do anything with statement (1) is to subtract 2xy
from both sides:
x^2 - 2xy + y^2 = 1
(x - y)(x - y) = 1
x - y = 1 or x - y = -1
There are an in…nite number of possible solutions for x and y, so there’s no
way to determine a speci…c value for x^2 + y^2.
Statement (2) is insufficient for similar reasons:
x^2 + y^2 = 4 - 2xy
x^2 + 2xy + y^2 = 4
(x + y)(x + y) = 4
x + y = 2 or x + y = -2
Again, there are an in…nite number of possibilities for x and y.
Taken together, you still don’t have enough information. If you had exactly
two equations (such as x-y = 1 and x+y = 2), you could solve, but you have
two diferent pairs of possible equations, which is insufficient to …find the values
of the variables. Choice (E) is correct.
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Nov 2014, 01:44, edited 6 times in total.
Edited the OA.
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34817
Followers: 6476

Kudos [?]: 82543 [3] , given: 10107

Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 23 Nov 2012, 07:41
3
This post received
KUDOS
Expert's post
What is the value of x^2+y^2 ?

(1) x^2+y^2=2xy+1 --> \(x^2-2xy+y^2=1\) --> \((x-y)^2=1\). If \(x=1\) and \(y=0\), then \(x^2+y^2=1\) but if \(x=2\) and \(y=1\), then \(x^2+y^2=5\). Not sufficient.

(2) x^2+y^2=4-2xy --> \(x^2+2xy+y^2=4\) --> \((x+y)^2=4\). If \(x=2\) and \(y=0\), then \(x^2+y^2=4\) but if \(x=1\) and \(y=1\), then \(x^2+y^2=2\). Not sufficient.

(1)+(2) Sum the equations: \(2(x^2+y^2)=5\) --> \(x^2+y^2=2.5\). Sufficient.

Answer: C. OA must be wrong.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 26 Apr 2012
Posts: 34
Followers: 1

Kudos [?]: 8 [0], given: 27

GMAT ToolKit User
Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 23 Nov 2012, 07:46
Bunuel wrote:
What is the value of x^2+y^2 ?

(1) x^2+y^2=2xy+1 --> \(x^2-2xy+y^2=1\) --> \((x-y)^2=1\). If \(x=1\) and \(y=0\), then \(x^2+y^2=1\) but if \(x=2\) and \(y=1\), then \(x^2+y^2=5\). Not sufficient.

(2) x^2+y^2=4-2xy --> \(x^2+2xy+y^2=4\) --> \((x+y)^2=4\). If \(x=2\) and \(y=0\), then \(x^2+y^2=4\) but if \(x=1\) and \(y=1\), then \(x^2+y^2=2\). Not sufficient.

(1)+(2) Sum the equations: \(2(x^2+y^2)=5\) --> \(x^2+y^2=2.5\). Sufficient.

Answer: C. OA must be wrong.

Hope it's clear.



Thanks Bunuel!!! (I feel like a VIP having you respond to one of my questions!) haha

"C" is what I thought! I got worried and couldn't see what I was doing wrong even after reading the OA description.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34817
Followers: 6476

Kudos [?]: 82543 [0], given: 10107

Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 23 Nov 2012, 07:48
maxLRok wrote:
Bunuel wrote:
What is the value of x^2+y^2 ?

(1) x^2+y^2=2xy+1 --> \(x^2-2xy+y^2=1\) --> \((x-y)^2=1\). If \(x=1\) and \(y=0\), then \(x^2+y^2=1\) but if \(x=2\) and \(y=1\), then \(x^2+y^2=5\). Not sufficient.

(2) x^2+y^2=4-2xy --> \(x^2+2xy+y^2=4\) --> \((x+y)^2=4\). If \(x=2\) and \(y=0\), then \(x^2+y^2=4\) but if \(x=1\) and \(y=1\), then \(x^2+y^2=2\). Not sufficient.

(1)+(2) Sum the equations: \(2(x^2+y^2)=5\) --> \(x^2+y^2=2.5\). Sufficient.

Answer: C. OA must be wrong.

Hope it's clear.



Thanks Bunuel!!! (I feel like a VIP having you respond to one of my questions!) haha

"C" is what I thought! I got worried and couldn't see what I was doing wrong even after reading the OA description.


Can you please post their solution?
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 26 Apr 2012
Posts: 34
Followers: 1

Kudos [?]: 8 [0], given: 27

GMAT ToolKit User
Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 23 Nov 2012, 08:50
Bunuel wrote:
maxLRok wrote:
Bunuel wrote:
What is the value of x^2+y^2 ?

(1) x^2+y^2=2xy+1 --> \(x^2-2xy+y^2=1\) --> \((x-y)^2=1\). If \(x=1\) and \(y=0\), then \(x^2+y^2=1\) but if \(x=2\) and \(y=1\), then \(x^2+y^2=5\). Not sufficient.

(2) x^2+y^2=4-2xy --> \(x^2+2xy+y^2=4\) --> \((x+y)^2=4\). If \(x=2\) and \(y=0\), then \(x^2+y^2=4\) but if \(x=1\) and \(y=1\), then \(x^2+y^2=2\). Not sufficient.

(1)+(2) Sum the equations: \(2(x^2+y^2)=5\) --> \(x^2+y^2=2.5\). Sufficient.

Answer: C. OA must be wrong.

Hope it's clear.



Thanks Bunuel!!! (I feel like a VIP having you respond to one of my questions!) haha

"C" is what I thought! I got worried and couldn't see what I was doing wrong even after reading the OA description.


Can you please post their solution?



Just put it in the main post
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34817
Followers: 6476

Kudos [?]: 82543 [0], given: 10107

Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 23 Nov 2012, 08:56
maxLRok wrote:
Bunuel wrote:
maxLRok wrote:

Thanks Bunuel!!! (I feel like a VIP having you respond to one of my questions!) haha

"C" is what I thought! I got worried and couldn't see what I was doing wrong even after reading the OA description.


Can you please post their solution?



Just put it in the main post


Their solution is not correct.

Four pairs of (x,y) satisfy (x-y)^2=1 and (x+y)^2=4: (-3/2, -1/2), (-1/2, -3/2), (3/2, 1/2) and (1/2, 3/2). For each pair x^2+y^2=10/2.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 12 Dec 2013
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 5

Premium Member
Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 06 Jun 2014, 07:02
Hello Everyone,

This DS problem is from the Jeffrey Sackmann Challenge Algebra set, Quadratics. Not sure about the difficulty level.

What is the value of x^2 + y^2 ?
1) x^2 + y^2 = 2xy + 1
2) x^2 + y^2 = 4 - 2xy

The answer is (E) But I'm not sure why we didn't just use the two statements together > add them > 2xy cancels out and the answer would be: x^2 + y^2 = 5/2 ?

Thanks in advance :)
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34817
Followers: 6476

Kudos [?]: 82543 [1] , given: 10107

Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 06 Jun 2014, 07:08
1
This post received
KUDOS
Expert's post
Mfz83 wrote:
Hello Everyone,

This DS problem is from the Jeffrey Sackmann Challenge Algebra set, Quadratics. Not sure about the difficulty level.

What is the value of x^2 + y^2 ?
1) x^2 + y^2 = 2xy + 1
2) x^2 + y^2 = 4 - 2xy

The answer is (E) But I'm not sure why we didn't just use the two statements together > add them > 2xy cancels out and the answer would be: x^2 + y^2 = 5/2 ?

Thanks in advance :)


Merging similar topics. please refer to the discussion above.

You are right the OA must be C, instead of E.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rule 3. Thank you.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 17 Dec 2012
Posts: 31
Followers: 1

Kudos [?]: 14 [0], given: 34

Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 11 Jun 2014, 04:41
What is the value of \(x^2\) +\(y^2\)?

(1)\(x^2\) +\(y^2\) = \(2xy + 1\)

(1) \(x^2 +y^2 = 4 - 2xy\)

Last edited by Gnpth on 11 Jun 2014, 04:58, edited 1 time in total.
Updated the OA
1 KUDOS received
Moderator
Moderator
User avatar
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 677
Location: India
GMAT 1: 680 Q47 V34
Followers: 60

Kudos [?]: 915 [1] , given: 216

GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 11 Jun 2014, 05:01
1
This post received
KUDOS
irda wrote:
What is the value of \(x^2\) +\(y^2\)?

(1)\(x^2\) +\(y^2\) = \(2xy + 1\)

(1) \(x^2 +y^2 = 4 - 2xy\)



The question is already discussed here. Also the OA is wrong.

Before posting read the rules for posting.
_________________

Become a GMAT Club Premium member to avail lot of discounts

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11653
Followers: 527

Kudos [?]: 141 [0], given: 0

Premium Member
Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 06 Jul 2016, 04:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Director
Director
User avatar
Joined: 18 Oct 2014
Posts: 915
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Followers: 80

Kudos [?]: 172 [0], given: 69

GMAT ToolKit User CAT Tests
Re: What is the value of x^2 + y^2 ? [#permalink]

Show Tags

New post 06 Jul 2016, 06:39
maxLRok wrote:
What is the value of x^2 + y^2 ?

(1) x^2 + y^2 = 2xy+1
(2) x^2 + y^2 = 4 - 2xy



Statement 1 and 2 both do not give us the value of xy and hence are not sufficient to arrive at the answer

adding both statements

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

x^2 + y^2= 2.5

C is the answer
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Re: What is the value of x^2 + y^2 ?   [#permalink] 06 Jul 2016, 06:39
    Similar topics Author Replies Last post
Similar
Topics:
17 Experts publish their posts in the topic What is the value of x^2 - y^2? bulletpoint 10 20 Oct 2013, 06:32
2 Experts publish their posts in the topic What is the value of x^2 - 4y^2? derekgmat 3 08 Nov 2012, 03:10
2 Experts publish their posts in the topic What is the value of x^2 + y^2 ? metallicafan 7 26 Aug 2012, 09:56
Experts publish their posts in the topic What is the value of x^2 - y^2 ? redpearl 2 10 May 2012, 00:07
1 Experts publish their posts in the topic What is the value of x^2 + y^2 ? krazo 6 04 Oct 2010, 18:06
Display posts from previous: Sort by

What is the value of 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 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®.