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

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What is the value of x^2+y^2 ? [#permalink] New post 23 Nov 2012, 06:29
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53% (02:10) correct 47% (01:11) wrong based on 91 sessions
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 12 Sep 2013, 02:57, edited 5 times in total.
Edited the OA.
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Re: What is the value of x^2+y^2 ? [#permalink] New post 23 Nov 2012, 06:41
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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.
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Re: What is the value of x^2+y^2 ? [#permalink] New post 23 Nov 2012, 06:46
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.
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Re: What is the value of x^2+y^2 ? [#permalink] New post 23 Nov 2012, 06:48
Expert's post
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?
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Re: What is the value of x^2+y^2 ? [#permalink] New post 23 Nov 2012, 07:50
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
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Re: What is the value of x^2+y^2 ? [#permalink] New post 23 Nov 2012, 07:56
Expert's post
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.
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Quadratics [#permalink] New post 06 Jun 2014, 06:02
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 :)
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Re: Quadratics [#permalink] New post 06 Jun 2014, 06:08
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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.
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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.


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What is the value of x^2 +y^2 ? [#permalink] New post 11 Jun 2014, 03:41
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, 03:58, edited 1 time in total.
Updated the OA
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Re: What is the value of x^2 +y^2 ? [#permalink] New post 11 Jun 2014, 04:01
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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.

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Re: What is the value of x^2 +y^2 ?   [#permalink] 11 Jun 2014, 04:01
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