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What is the value of y?

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What is the value of y? [#permalink] New post 15 Dec 2012, 10:33
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What is the value of y?

(1) x^2 - y^2 = 5
(2) x and y are each positive integers
[Reveal] Spoiler: OA

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Re: what is the value of y? [#permalink] New post 16 Dec 2012, 01:52
JJ2014 wrote:
what is the value of y?

(1) x^2 - y^2 = 5
(2) x and y are each positive integers



Hi,

From 1, we get (x-y)(x+y)=5 i.e (x-y)=1,5 or (x+y)= 5,1...solving we get 2 values of y (one positive and one negative)

From 2 alone we get nothing

combining 1 & 2 we get X and Y as postive and we get one solution
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Re: what is the value of y? [#permalink] New post 16 Dec 2012, 07:06
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mridulparashar1 wrote:
JJ2014 wrote:
What is the value of y?

(1) x^2 - y^2 = 5
(2) x and y are each positive integers



Hi,

From 1, we get (x-y)(x+y)=5 i.e (x-y)=1,5 or (x+y)= 5,1...solving we get 2 values of y (one positive and one negative)

From 2 alone we get nothing

combining 1 & 2 we get X and Y as postive and we get one solution


The red part is not correct. From x^2 - y^2 = 5 we cannot say that x-y=1 and x+y=5 (or vise-versa) because for (1) we don't know whether x and y are integers. So, for example it's possible that x-y=10 and x+y=1/2. Even if we knew that x and y are integers, still from (x+y)(x-y)=5 it follows that x+y=5 and x-y=1 (or vise versa) OR x+y=-5 and x-y=-1 (or vise versa).

What is the value of y?

(1) x^2 - y^2 = 5. Infinitely many solutions exist for x and y. Not sufficient.

(2) x and y are each positive integers. Not sufficient.

(1)+(2) Since x and y are positive integers then x+y=integer>0 and x-y=integer AND x+y>x-y. Thus from x^2 - y^2 =(x+y)(x-y)= 5 we'd have that x+y=5 and x-y=1, from which it follows that y=2. Sufficient.

Answer: C.
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What is the value of y?? [#permalink] New post 28 Feb 2013, 21:07
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(1)x^{2}-y^{2}=5
(2) x and y are each positive integers.
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Re: What is the value of y?? [#permalink] New post 28 Feb 2013, 21:30
Did you want an explanation?
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Re: What is the value of y?? [#permalink] New post 28 Feb 2013, 22:28
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Did you want an explanation?


nope just posted the question! If you think its too easy please tag this question as sub 600
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Re: What is the value of y?? [#permalink] New post 28 Feb 2013, 22:32
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NonYankee wrote:
Did you want an explanation?


nope just posted the question! If you think its too easy please tag this question as sub 600


Ok. Thanks for contributing this problem! As for the difficulty, I have no gauge for the level of questions. :lol:
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Re: What is the value of y?? [#permalink] New post 28 Feb 2013, 22:36
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rajathpanta wrote:
NonYankee wrote:
Did you want an explanation?


nope just posted the question! If you think its too easy please tag this question as sub 600


Ok. Thanks for contributing this problem! As for the difficulty, I have no gauge for the level of questions. :lol:



:) we mere mortals talk in terms of difficulty level :) For you, its a different ball game! you should ask is this a sub-800 question?? LOL :P
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Re: What is the value of y?? [#permalink] New post 28 Feb 2013, 22:46
rajathpanta wrote:
:) we mere mortals talk in terms of difficulty level :) For you, its a different ball game! you should ask is this a sub-800 question?? LOL :P


Hahaha that made me literally laugh out loud!
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Re: What is the value of y?? [#permalink] New post 01 Mar 2013, 00:25
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Re: What is the value of y?? [#permalink] New post 01 Mar 2013, 00:27
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NonYankee wrote:
rajathpanta wrote:
NonYankee wrote:
Did you want an explanation?


nope just posted the question! If you think its too easy please tag this question as sub 600


Ok. Thanks for contributing this problem! As for the difficulty, I have no gauge for the level of questions. :lol:


I'd say that the difficulty level of this question is ~650.
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Re: What is the value of y? [#permalink] New post 01 Mar 2013, 06:29
Hi Bunuel,

It sounds stupid but can u tell me about this step:

X+y=5 and X-y=1. I always used to think that it will mean x+y=5 or x-y=5.
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Re: What is the value of y? [#permalink] New post 04 Mar 2013, 03:50
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shreerajp99 wrote:
Hi Bunuel,

It sounds stupid but can u tell me about this step:

X+y=5 and X-y=1. I always used to think that it will mean x+y=5 or x-y=5.


When we consider the two statements together we have that both x and y are positive integers, thus x+y=integer>0 and x-y=integer AND x+y>x-y.

Next, we also have that x^2 - y^2 =(x+y)(x-y)= 5, so we have that the product of two multiple, x+y and x-y is equal to 5, a prime number. Since x+y=integer>0 and x-y=integer, then x+y must be 5 AND x-y must be 1: 5*1=5.

Hope it's clear.
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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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Re: What is the value of y?   [#permalink] 04 Mar 2013, 03:50
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